Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challen...Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challenging tasks.The goal of subgraph matching is to find all subgraphs in the data graph that are isomorphic to the query graph.Traditional methods mostly rely on search strategies with high computational complexity and are hard to apply to large-scale real datasets.With the advent of graph neural networks(GNNs),researchers have turned to GNNs to address subgraph matching problems.However,the multi-attributed features on nodes and edges are overlooked during the learning of graphs,which causes inaccurate results in real-world scenarios.To tackle this problem,we propose a novel model called subgraph matching on multi-attributed graph network(SGMAN).SGMAN first utilizes improved line graphs to capture node and edge features.Then,SGMAN integrates GNN and contrastive learning(CL)to derive graph representation embeddings and calculate the matching matrix to represent the matching results.We conduct experiments on public datasets,and the results affirm the superior performance of our model.展开更多
Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when...Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.展开更多
With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have cho...With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.展开更多
The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular...The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.展开更多
Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph ma...Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph.展开更多
High-throughput techniques,such as the yeast-two-hybrid system,produce mass protein-protein interaction data. The new technique makes it possible to predict protein complexes by com-putation. A novel method,named DSDA...High-throughput techniques,such as the yeast-two-hybrid system,produce mass protein-protein interaction data. The new technique makes it possible to predict protein complexes by com-putation. A novel method,named DSDA,has been put forward to predict protein complexes via dense subgraph because the proteins among a protein complex have a much tighter relation among them than with others. This method chooses a node with its neighbors to form the initial subgraph,and chooses a node which has the tightest relation with the subgraph according to greedy strategy,then the chosen node is added into the initial subgraph until the subgraph density is below the threshold value. The ob-tained subgraph is then removed from the network and the process continues until no subgraph can be detected. Compared with other algorithms,DSDA can predict not only non-overlap protein com-plexes but also overlap protein complexes. The experiment results show that DSDA predict as many protein complexes as possible. And in Y78K network the accuracy of DSDA is as twice times as that of RNSC and MCL.展开更多
Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that ...Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that K n-R n-1 has a star ascending subgraph decomposition,here K n is the complete graph with order n and R n-1 is a subgraph of K n with size at most n-1. In paper [3],Ma Kejie and Chen Huaitang proved that K n-R n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K n-R n-1 has a comet ascending subgraph decomposition.展开更多
Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a gi...Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a given cardinality from networks (or connected undirected graphs in networks). The first algorithm is a variant of a previous wellknown algorithm. The algorithm enumerates all connected induced subgraphs of cardinality k in a bottom-up manner. Thedata structures that lead to unit time element checking and linear space are presented. Different from previous algorithmsthat work in either a bottom-up manner or a reverse search manner, an algorithm that enumerates all connected inducedsubgraphs of cardinality k in a top-down manner is proposed. The correctness and complexity of the top-down algorithmare theoretically analyzed and proven. In the experiments, we evaluate the efficiency of the algorithms using a set of realworld networks from various fields. Experimental results show that the variant bottom-up algorithm outperforms thestate-of-the-art algorithms for enumerating connected induced subgraphs of small cardinality, and the top-down algorithmcan achieve an order of magnitude speedup over the state-of-the-art algorithms for enumerating connected induced subgraphs of large cardinality.展开更多
Given integers m and f,let Sn(m,f)be the set consisting of all integers e such that every n-vertex graph with e edges contains an m-vertex induced subgraph with f edges,and let σ(m,f)=lim sup_(n→∞)|S_(n)(m,f)|/(_(2...Given integers m and f,let Sn(m,f)be the set consisting of all integers e such that every n-vertex graph with e edges contains an m-vertex induced subgraph with f edges,and let σ(m,f)=lim sup_(n→∞)|S_(n)(m,f)|/(_(2)^(n)).As a natural extension of an extremal problem of Erdös,this was investigated by Erd˝os,Füredi,Rothschild and Sós 20 years ago.Their main result indicates that integers in S_(n)(m,f)are rare for most pairs(m,f),though they also found infinitely many pairs(m,f)whose σ(m,f)is a fixed positive constant.Here we aim to provide some improvements on this study.Our first result shows that σ(m,f)≤1/2 holds for all but finitely many pairs(m,f)and the constant 1/2 cannot be improved.This answers a question of Erdös et al.Our second result considers infinitely many pairs(m,f)of special forms,whose exact values of σ(m,f)were conjectured by Erdös et al.We partially solve this conjecture(only leaving two open cases)by making progress on some constructions which are related to number theory.Our proofs are based on the research of Erdös et al.and involve different arguments in number theory.We also discuss some related problems.展开更多
The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has ...The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has a wide range of applications including question answering and semantic search.In this paper,we study the problem of subgraph matching on knowledge graph.Specifically,given a query graph q and a data graph G,the problem of subgraph matching is to conduct all possible subgraph isomorphic mappings of q on G.Knowledge graph is formed as a directed labeled multi-graph having multiple edges between a pair of vertices and it has more dense semantic and structural features than general graph.To accelerate subgraph matching on knowledge graph,we propose a novel subgraph matching algorithm based on subgraph index for knowledge graph,called as FGqT-Match.The subgraph matching algorithm consists of two key designs.One design is a subgraph index of matching-driven flow graph(FGqT),which reduces redundant calculations in advance.Another design is a multi-label weight matrix,which evaluates a near-optimal matching tree for minimizing the intermediate candidates.With the aid of these two key designs,all subgraph isomorphic mappings are quickly conducted only by traversing FGqj.Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms.展开更多
To meet the urgent requirement of enterprises for three-dimensional (3D) process models, an approach based on subgraph isomorphism is proposed to solve the matching problem between precursory 3D process model and 2D w...To meet the urgent requirement of enterprises for three-dimensional (3D) process models, an approach based on subgraph isomorphism is proposed to solve the matching problem between precursory 3D process model and 2D working procedure drawings. First, the projection drawings of the precursory 3D process model are obtained, then the primitives are extracted and the attributed adjacency graph (AAG) is constructed. Finally, by taking the 2D working procedure drawing as the AAG, and the projection drawing as the whole AAG, the matching problem between precursory 3D process model and 2D working procedure drawings is translated into the problem of subgraph isomorphism. To raise the matching efficiency, the AAG is partitioned, and the vertexes of the graph are classified effectively using the vertex’s attributes. Experimental results show that this method is able to support exact match and the matching efficiency can meet the requirement of practical applications.展开更多
An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, w...An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, which are the foundations for many applications including semantic searching, ontology matching, and linked data analysis. However, since different ontologies have different preferences to describe their elements, obtaining the semantic context of an element is an open problem. A semantic subgraph was proposed to capture the real meanings of ontology elements. To extract the semantic subgraphs, a hybrid ontology graph is used to represent the semantic relations between elements. An extracting algorithm based on an electrical circuit model is then used with new conductivity calculation rules to improve the quality of the semantic subgraphs. The evaluation results show that the semantic subgraphs properly capture the local meanings of elements. Ontology matching based on semantic subgraphs also demonstrates that the semantic subgraph is a promising technique for ontology applications.展开更多
Acid-base dissociation constant(pK_(a)) is a key physicochemical parameter in chemical science, especially in organic synthesis and drug discovery. Current methodologies for pK_(a) prediction still suffer from limited...Acid-base dissociation constant(pK_(a)) is a key physicochemical parameter in chemical science, especially in organic synthesis and drug discovery. Current methodologies for pK_(a) prediction still suffer from limited applicability domain and lack of chemical insight. Here we present MF-SuP-pK_(a)(multi-fidelity modeling with subgraph pooling for pK_(a) prediction), a novel pK_(a) prediction model that utilizes subgraph pooling, multi-fidelity learning and data augmentation. In our model, a knowledgeaware subgraph pooling strategy was designed to capture the local and global environments around the ionization sites for micro-pK_(a) prediction. To overcome the scarcity of accurate pK_(a) data, lowfidelity data(computational pK_(a)) was used to fit the high-fidelity data(experimental pK_(a)) through transfer learning. The final MF-SuP-pK_(a) model was constructed by pre-training on the augmented ChEMBL data set and fine-tuning on the DataWarrior data set. Extensive evaluation on the DataWarrior data set and three benchmark data sets shows that MF-SuP-pK_(a) achieves superior performances to the state-of-theart pK_(a) prediction models while requires much less high-fidelity training data. Compared with Attentive FP, MF-SuP-pK_(a) achieves 23.83% and 20.12% improvement in terms of mean absolute error(MAE) on the acidic and basic sets, respectively.展开更多
To solve the problem of grid coarse-grained reconfigurable array task mapping under multiple constraints,we propose a Loop Subgraph-Level Greedy Mapping(LSLGM)algorithm using parallelism and processing element fragmen...To solve the problem of grid coarse-grained reconfigurable array task mapping under multiple constraints,we propose a Loop Subgraph-Level Greedy Mapping(LSLGM)algorithm using parallelism and processing element fragmentation.Under the constraint of a reconfigurable array,the LSLGM algorithm schedules node from a ready queue to the current reconfigurable cell array block.After mapping a node,its successor’s indegree value will be dynamically updated.If its successor’s indegree is zero,it will be directly scheduled to the ready queue;otherwise,the predecessor must be dynamically checked.If the predecessor cannot be mapped,it will be scheduled to a blocking queue.To dynamically adjust the ready node scheduling order,the scheduling function is constructed by exploiting factors,such as node number,node level,and node dependency.Compared with the loop subgraph-level mapping algorithm,experimental results show that the total cycles of the LSLGM algorithm decreases by an average of 33.0%(PEA44)and 33.9%(PEA_(7×7)).Compared with the epimorphism map algorithm,the total cycles of the LSLGM algorithm decrease by an average of 38.1%(PEA_(4×4))and 39.0%(PEA_(7×7)).The feasibility of LSLGM is verified.展开更多
Because of its wide application, the subgraph matching problem has been studied extensively during the past decade. However, most existing solutions assume that a data graph is a vertex/edge-labeled graph （i.e., each...Because of its wide application, the subgraph matching problem has been studied extensively during the past decade. However, most existing solutions assume that a data graph is a vertex/edge-labeled graph （i.e., each vertex/edge has a simple label）. These solutions build structural indices by considering the vertex labels. However, some real graphs contain rich-content vertices such as user profiles in social networks and HTML pages on the World Wide Web. In this study, we consider the problem of subgraph matching using a more general scenario. We build a structural index that does not depend on any vertex content. Based on the index, we design a holistic subgraph matching algorithm that considers the query graph as a whole and finds one match at a time. In order to further improve efficiency, we propose a ＂partial evaluation and assembly＂ framework to find sub- graph matches over large graphs. Last but not least, our index has light maintenance overhead. Therefore, our method can work well on dynamic graphs. Extensive experiments on real graphs show that our method outperforms the state-of-the-art algorithms.展开更多
A Mechanism-Inferring method of networks exploited from machine learning theory caneffectively evaluate the predicting performance of a network model.The existing method for inferringnetwork mechanisms based on a cens...A Mechanism-Inferring method of networks exploited from machine learning theory caneffectively evaluate the predicting performance of a network model.The existing method for inferringnetwork mechanisms based on a census of subgraph numbers has some drawbacks,especially the needfor a runtime increasing strongly with network size and network density.In this paper,an improvedmethod has been proposed by introducing a census algorithm of subgraph concentrations.Networkmechanism can be quickly inferred by the new method even though the network has large scale andhigh density.Therefore,the application perspective of mechanism-inferring method has been extendedinto the wider fields of large-scale complex networks.By applying the new method to a case of proteininteraction network,the authors obtain the same inferring result as the existing method,which approvesthe effectiveness of the method.展开更多
To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multieasts in wireless...To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multieasts in wireless networks. We propose two suboptimal algorithms as extensions of the Steiner tree multicast. The critical 1-cut path eliminating （C1CPE） algorithm attempts to find the minimum-cost solution for the coexistence of two multicast trees with the same throughput by reusing the links in the topology, and keeps the solution decodable by a coloring process. For the special case in which the two multicast trees share the same source and destinations, we propose the extended selective closest terminal first （E-SCTF） algorithm out of the CICPE algorithm. Theoretically the complexity of the E-SCTF algorithm is lower than that of the C1CPE algorithm. Simulation results show that both algorithms have superior performance in terms of power cost and that the advantage is more evident in networks with ultra-densification.展开更多
Graph data mining has been a crucial as well as inevitable area of research.Large amounts of graph data are produced in many areas,such as Bioinformatics,Cheminformatics,Social Networks,etc.Scalable graph data mining ...Graph data mining has been a crucial as well as inevitable area of research.Large amounts of graph data are produced in many areas,such as Bioinformatics,Cheminformatics,Social Networks,etc.Scalable graph data mining methods are getting increasingly popular and necessary due to increased graph complexities.Frequent subgraph mining is one such area where the task is to find overly recurring patterns/subgraphs.To tackle this problem,many main memory-based methods were proposed,which proved to be inefficient as the data size grew exponentially over time.In the past few years,several research groups have attempted to handle the Frequent Subgraph Mining(FSM)problem in multiple ways.Many authors have tried to achieve better performance using Graphic Processing Units(GPUs)which has multi-fold improvement over in-memory while dealing with large datasets.Later,Google’s MapReduce model with the Hadoop framework proved to be a major breakthrough in high performance large batch processing.Although MapReduce came with many benefits,its disk I/O and noniterative style model could not help much for FSM domain since subgraph mining process is an iterative approach.In recent years,Spark has emerged to be the De Facto industry standard with its distributed in-memory computing capability.This is a right fit solution for iterative style of programming as well.In this survey,we cover how high-performance computing has helped in improving the performance tremendously in the transactional directed and undirected aspect of graphs and performance comparisons of various FSM techniques are done based on experimental results.展开更多
The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G...The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.展开更多
文摘Graphs have been widely used in fields ranging from chemical informatics to social network analysis.Graph-related problems become increasingly significant,with subgraph matching standing out as one of the most challenging tasks.The goal of subgraph matching is to find all subgraphs in the data graph that are isomorphic to the query graph.Traditional methods mostly rely on search strategies with high computational complexity and are hard to apply to large-scale real datasets.With the advent of graph neural networks(GNNs),researchers have turned to GNNs to address subgraph matching problems.However,the multi-attributed features on nodes and edges are overlooked during the learning of graphs,which causes inaccurate results in real-world scenarios.To tackle this problem,we propose a novel model called subgraph matching on multi-attributed graph network(SGMAN).SGMAN first utilizes improved line graphs to capture node and edge features.Then,SGMAN integrates GNN and contrastive learning(CL)to derive graph representation embeddings and calculate the matching matrix to represent the matching results.We conduct experiments on public datasets,and the results affirm the superior performance of our model.
基金Supported by the National Natural Science Foundation of China(10701065 and 11101378)Zhejiang Provincial Natural Science Foundation(LY14A010009)
文摘Bollobas and Gyarfas conjectured that for n 〉 4（k - 1） every 2-edge-coloring of Kn contains a monochromatic k-connected subgraph with at least n - 2k ＋ 2 vertices. Liu, et al. proved that the conjecture holds when n 〉 13k - 15. In this note, we characterize all the 2-edge-colorings of Kn where each monochromatic k-connected subgraph has at most n - 2k ＋ 2 vertices for n ≥ 13k - 15.
基金supported by the State Grid Science and Technology Project (Title: Research on High Performance Analysis Technology of Power Grid GIS Topology Based on Graph Database, 5455HJ160005)
文摘With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.
文摘The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.
文摘Subgraph matching problem is identifying a target subgraph in a graph. Graph neural network (GNN) is an artificial neural network model which is capable of processing general types of graph structured data. A graph may contain many subgraphs isomorphic to a given target graph. In this paper GNN is modeled to identify a subgraph that matches the target graph along with its characteristics. The simulation results show that GNN is capable of identifying a target sub-graph in a graph.
基金Supported by the National Natural Science Foundation of China (60803025)
文摘High-throughput techniques,such as the yeast-two-hybrid system,produce mass protein-protein interaction data. The new technique makes it possible to predict protein complexes by com-putation. A novel method,named DSDA,has been put forward to predict protein complexes via dense subgraph because the proteins among a protein complex have a much tighter relation among them than with others. This method chooses a node with its neighbors to form the initial subgraph,and chooses a node which has the tightest relation with the subgraph according to greedy strategy,then the chosen node is added into the initial subgraph until the subgraph density is below the threshold value. The ob-tained subgraph is then removed from the network and the process continues until no subgraph can be detected. Compared with other algorithms,DSDA can predict not only non-overlap protein com-plexes but also overlap protein complexes. The experiment results show that DSDA predict as many protein complexes as possible. And in Y78K network the accuracy of DSDA is as twice times as that of RNSC and MCL.
文摘Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that K n-R n-1 has a star ascending subgraph decomposition,here K n is the complete graph with order n and R n-1 is a subgraph of K n with size at most n-1. In paper [3],Ma Kejie and Chen Huaitang proved that K n-R n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K n-R n-1 has a comet ascending subgraph decomposition.
基金supported by the National Natural Science Foundation of China under Grant No.61404069the Scientific Research Project of Colleges and Universities in Guangdong Province of China under Grant No.2021ZDZX1027+1 种基金the Guangdong Basic and Applied Basic Research Foundation under Grant Nos.2022A1515110712 and 2023A1515010077the STU Scientific Research Foundation for Talents under Grant Nos.NTF20016 and NTF20017.
文摘Mining subgraphs with interesting structural properties from networks (or graphs) is a computationally challenging task. In this paper, we propose two algorithms for enumerating all connected induced subgraphs of a given cardinality from networks (or connected undirected graphs in networks). The first algorithm is a variant of a previous wellknown algorithm. The algorithm enumerates all connected induced subgraphs of cardinality k in a bottom-up manner. Thedata structures that lead to unit time element checking and linear space are presented. Different from previous algorithmsthat work in either a bottom-up manner or a reverse search manner, an algorithm that enumerates all connected inducedsubgraphs of cardinality k in a top-down manner is proposed. The correctness and complexity of the top-down algorithmare theoretically analyzed and proven. In the experiments, we evaluate the efficiency of the algorithms using a set of realworld networks from various fields. Experimental results show that the variant bottom-up algorithm outperforms thestate-of-the-art algorithms for enumerating connected induced subgraphs of small cardinality, and the top-down algorithmcan achieve an order of magnitude speedup over the state-of-the-art algorithms for enumerating connected induced subgraphs of large cardinality.
基金supported by Hong Kong RGC Grant GRF 16308219 and Hong Kong RGC Grant ECS 26304920supported by the National Key R and D Program of China 2020YFA0713100+4 种基金National Natural Science Foundation of China Grant 12125106Innovation Program for Quantum Science and Technology 2021ZD0302904Anhui Initiative in Quantum Information Technologies Grant AHY150200Research supported in part by NSFC Grant 11922113National Key Research and Development Program of China 2021YFA1000700.
文摘Given integers m and f,let Sn(m,f)be the set consisting of all integers e such that every n-vertex graph with e edges contains an m-vertex induced subgraph with f edges,and let σ(m,f)=lim sup_(n→∞)|S_(n)(m,f)|/(_(2)^(n)).As a natural extension of an extremal problem of Erdös,this was investigated by Erd˝os,Füredi,Rothschild and Sós 20 years ago.Their main result indicates that integers in S_(n)(m,f)are rare for most pairs(m,f),though they also found infinitely many pairs(m,f)whose σ(m,f)is a fixed positive constant.Here we aim to provide some improvements on this study.Our first result shows that σ(m,f)≤1/2 holds for all but finitely many pairs(m,f)and the constant 1/2 cannot be improved.This answers a question of Erdös et al.Our second result considers infinitely many pairs(m,f)of special forms,whose exact values of σ(m,f)were conjectured by Erdös et al.We partially solve this conjecture(only leaving two open cases)by making progress on some constructions which are related to number theory.Our proofs are based on the research of Erdös et al.and involve different arguments in number theory.We also discuss some related problems.
基金the National Natural Science Foundation of China(Grant Nos.61976032,62002039).
文摘The problem of subgraph matching is one fundamental issue in graph search,which is NP-Complete problem.Recently,subgraph matching has become a popular research topic in the field of knowledge graph analysis,which has a wide range of applications including question answering and semantic search.In this paper,we study the problem of subgraph matching on knowledge graph.Specifically,given a query graph q and a data graph G,the problem of subgraph matching is to conduct all possible subgraph isomorphic mappings of q on G.Knowledge graph is formed as a directed labeled multi-graph having multiple edges between a pair of vertices and it has more dense semantic and structural features than general graph.To accelerate subgraph matching on knowledge graph,we propose a novel subgraph matching algorithm based on subgraph index for knowledge graph,called as FGqT-Match.The subgraph matching algorithm consists of two key designs.One design is a subgraph index of matching-driven flow graph(FGqT),which reduces redundant calculations in advance.Another design is a multi-label weight matrix,which evaluates a near-optimal matching tree for minimizing the intermediate candidates.With the aid of these two key designs,all subgraph isomorphic mappings are quickly conducted only by traversing FGqj.Extensive empirical studies on real and synthetic graphs demonstrate that our techniques outperform the state-of-the-art algorithms.
基金supported by the National Natural Science Foundation of China (Grant No. 51075336)the National High Technology Research and Development Program of China (Grant No. 2007AA04Z137)
文摘To meet the urgent requirement of enterprises for three-dimensional (3D) process models, an approach based on subgraph isomorphism is proposed to solve the matching problem between precursory 3D process model and 2D working procedure drawings. First, the projection drawings of the precursory 3D process model are obtained, then the primitives are extracted and the attributed adjacency graph (AAG) is constructed. Finally, by taking the 2D working procedure drawing as the AAG, and the projection drawing as the whole AAG, the matching problem between precursory 3D process model and 2D working procedure drawings is translated into the problem of subgraph isomorphism. To raise the matching efficiency, the AAG is partitioned, and the vertexes of the graph are classified effectively using the vertex’s attributes. Experimental results show that this method is able to support exact match and the matching efficiency can meet the requirement of practical applications.
基金Supported by the National High-Tech Research and Development (863) Program of China (No.2009AA01Z147)the National Natural Science Foundation of China (Nos.61003156 and 90818027)the National Key Basic Research and Development (973) Program of China (No.2009CB320703)
文摘An element may have heterogeneous semantic interpretations in different ontologies. Therefore, understanding the real local meanings of elements is very useful for ontology operations such as querying and reasoning, which are the foundations for many applications including semantic searching, ontology matching, and linked data analysis. However, since different ontologies have different preferences to describe their elements, obtaining the semantic context of an element is an open problem. A semantic subgraph was proposed to capture the real meanings of ontology elements. To extract the semantic subgraphs, a hybrid ontology graph is used to represent the semantic relations between elements. An extracting algorithm based on an electrical circuit model is then used with new conductivity calculation rules to improve the quality of the semantic subgraphs. The evaluation results show that the semantic subgraphs properly capture the local meanings of elements. Ontology matching based on semantic subgraphs also demonstrates that the semantic subgraph is a promising technique for ontology applications.
基金financially supported by National Key Research and Development Program of China (2021YFF1201400)National Natural Science Foundation of China (22220102001)Natural Science Foundation of Zhejiang Province (LZ19H300001, LD22H300001, China)。
文摘Acid-base dissociation constant(pK_(a)) is a key physicochemical parameter in chemical science, especially in organic synthesis and drug discovery. Current methodologies for pK_(a) prediction still suffer from limited applicability domain and lack of chemical insight. Here we present MF-SuP-pK_(a)(multi-fidelity modeling with subgraph pooling for pK_(a) prediction), a novel pK_(a) prediction model that utilizes subgraph pooling, multi-fidelity learning and data augmentation. In our model, a knowledgeaware subgraph pooling strategy was designed to capture the local and global environments around the ionization sites for micro-pK_(a) prediction. To overcome the scarcity of accurate pK_(a) data, lowfidelity data(computational pK_(a)) was used to fit the high-fidelity data(experimental pK_(a)) through transfer learning. The final MF-SuP-pK_(a) model was constructed by pre-training on the augmented ChEMBL data set and fine-tuning on the DataWarrior data set. Extensive evaluation on the DataWarrior data set and three benchmark data sets shows that MF-SuP-pK_(a) achieves superior performances to the state-of-theart pK_(a) prediction models while requires much less high-fidelity training data. Compared with Attentive FP, MF-SuP-pK_(a) achieves 23.83% and 20.12% improvement in terms of mean absolute error(MAE) on the acidic and basic sets, respectively.
基金This research was supported by the Natural Science Foundation of Anhui Province(No.1808085MF203)the Natural Science Foundation of China(Nos.61972438 and 61432017).
文摘To solve the problem of grid coarse-grained reconfigurable array task mapping under multiple constraints,we propose a Loop Subgraph-Level Greedy Mapping(LSLGM)algorithm using parallelism and processing element fragmentation.Under the constraint of a reconfigurable array,the LSLGM algorithm schedules node from a ready queue to the current reconfigurable cell array block.After mapping a node,its successor’s indegree value will be dynamically updated.If its successor’s indegree is zero,it will be directly scheduled to the ready queue;otherwise,the predecessor must be dynamically checked.If the predecessor cannot be mapped,it will be scheduled to a blocking queue.To dynamically adjust the ready node scheduling order,the scheduling function is constructed by exploiting factors,such as node number,node level,and node dependency.Compared with the loop subgraph-level mapping algorithm,experimental results show that the total cycles of the LSLGM algorithm decreases by an average of 33.0%(PEA44)and 33.9%(PEA_(7×7)).Compared with the epimorphism map algorithm,the total cycles of the LSLGM algorithm decrease by an average of 38.1%(PEA_(4×4))and 39.0%(PEA_(7×7)).The feasibility of LSLGM is verified.
基金This work was partially supported by the National Key Research and Development Program of China （2016YFB1000603）, Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China （Grant Nos. 61622201, 61472131, and 61272546）, and Science and Technology Key Projects of Hunan Province （2015 TP1004）.
文摘Because of its wide application, the subgraph matching problem has been studied extensively during the past decade. However, most existing solutions assume that a data graph is a vertex/edge-labeled graph （i.e., each vertex/edge has a simple label）. These solutions build structural indices by considering the vertex labels. However, some real graphs contain rich-content vertices such as user profiles in social networks and HTML pages on the World Wide Web. In this study, we consider the problem of subgraph matching using a more general scenario. We build a structural index that does not depend on any vertex content. Based on the index, we design a holistic subgraph matching algorithm that considers the query graph as a whole and finds one match at a time. In order to further improve efficiency, we propose a ＂partial evaluation and assembly＂ framework to find sub- graph matches over large graphs. Last but not least, our index has light maintenance overhead. Therefore, our method can work well on dynamic graphs. Extensive experiments on real graphs show that our method outperforms the state-of-the-art algorithms.
基金supported by the National Natural Science Foundation of China under Grant No. 70401019
文摘A Mechanism-Inferring method of networks exploited from machine learning theory caneffectively evaluate the predicting performance of a network model.The existing method for inferringnetwork mechanisms based on a census of subgraph numbers has some drawbacks,especially the needfor a runtime increasing strongly with network size and network density.In this paper,an improvedmethod has been proposed by introducing a census algorithm of subgraph concentrations.Networkmechanism can be quickly inferred by the new method even though the network has large scale andhigh density.Therefore,the application perspective of mechanism-inferring method has been extendedinto the wider fields of large-scale complex networks.By applying the new method to a case of proteininteraction network,the authors obtain the same inferring result as the existing method,which approvesthe effectiveness of the method.
基金Proje ct supported by the National Natural Science Foundation of China(No.61571055)the Fund of SKL of MMW(No.K201815)the Important National Science&Technology Specific Projects(No.20 17ZX03001028)
文摘To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multieasts in wireless networks. We propose two suboptimal algorithms as extensions of the Steiner tree multicast. The critical 1-cut path eliminating （C1CPE） algorithm attempts to find the minimum-cost solution for the coexistence of two multicast trees with the same throughput by reusing the links in the topology, and keeps the solution decodable by a coloring process. For the special case in which the two multicast trees share the same source and destinations, we propose the extended selective closest terminal first （E-SCTF） algorithm out of the CICPE algorithm. Theoretically the complexity of the E-SCTF algorithm is lower than that of the C1CPE algorithm. Simulation results show that both algorithms have superior performance in terms of power cost and that the advantage is more evident in networks with ultra-densification.
文摘Graph data mining has been a crucial as well as inevitable area of research.Large amounts of graph data are produced in many areas,such as Bioinformatics,Cheminformatics,Social Networks,etc.Scalable graph data mining methods are getting increasingly popular and necessary due to increased graph complexities.Frequent subgraph mining is one such area where the task is to find overly recurring patterns/subgraphs.To tackle this problem,many main memory-based methods were proposed,which proved to be inefficient as the data size grew exponentially over time.In the past few years,several research groups have attempted to handle the Frequent Subgraph Mining(FSM)problem in multiple ways.Many authors have tried to achieve better performance using Graphic Processing Units(GPUs)which has multi-fold improvement over in-memory while dealing with large datasets.Later,Google’s MapReduce model with the Hadoop framework proved to be a major breakthrough in high performance large batch processing.Although MapReduce came with many benefits,its disk I/O and noniterative style model could not help much for FSM domain since subgraph mining process is an iterative approach.In recent years,Spark has emerged to be the De Facto industry standard with its distributed in-memory computing capability.This is a right fit solution for iterative style of programming as well.In this survey,we cover how high-performance computing has helped in improving the performance tremendously in the transactional directed and undirected aspect of graphs and performance comparisons of various FSM techniques are done based on experimental results.
基金supported by the National Natural Science Foundation of China(No.11871398)the Natural Science Basic Research Plan in Shaanxi Province of China(Program No.2018JM1032)+1 种基金the Fundamental Research Funds for the Central Universities(No.3102019ghjd003)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.ZZ2019031)
文摘The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.
