The key issue in top-k retrieval, finding a set of k documents （from a large document collection） that can best answer a user＇s query, is to strike the optimal balance between relevance and diversity. In this paper...The key issue in top-k retrieval, finding a set of k documents （from a large document collection） that can best answer a user＇s query, is to strike the optimal balance between relevance and diversity. In this paper, we study the top-k re- trieval problem in the framework of facility location analysis and prove he submodularity of that objective function which provides a theoretical approximation guarantee of factor 1 -1/ε for the （best-first） greedy search algorithm. Furthermore, we propose a two-stage hybrid search strategy which first ob- tains a high-quality initial set of top-k documents via greedy search, and then refines that result set iteratively via local search. Experiments on two large TREC benchmark datasets show that our two-stage hybrid search strategy approach can supersede the existing ones effectively and efficiently.展开更多
In many kinds of games with economic significance,it is very important to study the submodularity of functions.In this paper,wemainly study the problem of maximizing a concave function over an intersection of two matr...In many kinds of games with economic significance,it is very important to study the submodularity of functions.In this paper,wemainly study the problem of maximizing a concave function over an intersection of two matroids.We obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some conditions.Moreover,we also present examples showing that these conditions can be satisfied.展开更多
Alzheimer’s disease(AD)is a neurological disorder that predominantly affects the brain.In the coming years,it is expected to spread rapidly,with limited progress in diagnostic techniques.Various machine learning(ML)a...Alzheimer’s disease(AD)is a neurological disorder that predominantly affects the brain.In the coming years,it is expected to spread rapidly,with limited progress in diagnostic techniques.Various machine learning(ML)and artificial intelligence(AI)algorithms have been employed to detect AD using single-modality data.However,recent developments in ML have enabled the application of these methods to multiple data sources and input modalities for AD prediction.In this study,we developed a framework that utilizes multimodal data(tabular data,magnetic resonance imaging(MRI)images,and genetic information)to classify AD.As part of the pre-processing phase,we generated a knowledge graph from the tabular data and MRI images.We employed graph neural networks for knowledge graph creation,and region-based convolutional neural network approach for image-to-knowledge graph generation.Additionally,we integrated various explainable AI(XAI)techniques to interpret and elucidate the prediction outcomes derived from multimodal data.Layer-wise relevance propagation was used to explain the layer-wise outcomes in the MRI images.We also incorporated submodular pick local interpretable model-agnostic explanations to interpret the decision-making process based on the tabular data provided.Genetic expression values play a crucial role in AD analysis.We used a graphical gene tree to identify genes associated with the disease.Moreover,a dashboard was designed to display XAI outcomes,enabling experts and medical professionals to easily comprehend the predic-tion results.展开更多
Maximizing the spread of influence is to select a set of seeds with specified size to maximize the spread of influence under a certain diffusion model in a social network. In the actual spread process, the activated p...Maximizing the spread of influence is to select a set of seeds with specified size to maximize the spread of influence under a certain diffusion model in a social network. In the actual spread process, the activated probability of node increases with its newly increasing activated neighbors, which also decreases with time. In this paper, we focus on the problem that selects k seeds based on the cascade model with diffusion decay to maximize the spread of influence in social networks. First, we extend the independent cascade model to incorporate the diffusion decay factor, called as the cascade model with diffusion decay and abbreviated as CMDD. Then, we discuss the objective function of maximizing the spread of influence under the CMDD, which is NP-hard. We further prove the monotonicity and submodularity of this objective function. Finally, we use the greedy algorithm to approximate the optimal result with the ration of 1 ? 1/e.展开更多
There exist two or more competing products in viral marketing, and the companies can exploit the social interactions of users to propagate the awareness of products. In this paper, we focus on selecting seeds for maxi...There exist two or more competing products in viral marketing, and the companies can exploit the social interactions of users to propagate the awareness of products. In this paper, we focus on selecting seeds for maximizing the competitive influence spread in social networks. First, we establish the possible graphs based on the propagation probability of edges, and then we use the competitive influence spread model (CISM) to model the competitive spread under the possible graph. Further, we consider the objective function of selecting k seeds of one product under the CISM when the seeds of another product have been known, which is monotone and submodular, and thus we use the CELF (cost-effective lazy forward) algorithm to accelerate the greedy algorithm that can approximate the optimal with 1 ? 1/e. Experimental results verify the feasibility and effectiveness of our method.展开更多
In remote terrestrial-satellite networks, caching is a very promising technique to alleviate the burden of space cloudlet(e.g., cache-enabled satellite user terminal) and to improve subscribers' quality of experie...In remote terrestrial-satellite networks, caching is a very promising technique to alleviate the burden of space cloudlet(e.g., cache-enabled satellite user terminal) and to improve subscribers' quality of experience(Qo E) in terms of buffering delay and achievable video streaming rate. In this paper, we studied a Qo E-driven caching placement optimization problem for video streaming that takes into account the required video streaming rate and the social relationship among users. Social ties between users are used to designate a set of helpers with caching capability, which can cache popular files proactively when the cloudlet is idle. We model the utility function of Qo E as a logarithmic function. Then, the caching placement problem is formulated as an optimization problem to maximize the user's average Qo E subject to the storage capacity constraints of the helpers and the cloudlets. Furthermore, we reformulate the problem into a monotone submodular optimization problem with a partition matroid constraint, and an efficient greedy algorithm with 1-1 e approximation ratio is proposed to solve it. Simulation results show that the proposed caching placement approach significantly outperforms the traditional approaches in terms of Qo E, while yields about the same delay and hit ratio performance compare to the delay-minimized scheme.展开更多
Netessine and Rudi（2003） consider a consumer-driven substitution problem with an arbitrary number of products under both centralized management and competition. They obtain analytically tractable solutions, establis...Netessine and Rudi（2003） consider a consumer-driven substitution problem with an arbitrary number of products under both centralized management and competition. They obtain analytically tractable solutions, establish concavity of the objective function, i.e., the expected profit function generated by each product and uniqueness of the equilibrium for the decentralize case. For the centralized case, they indicate that the objective function, i.e., the expected profit function, might not be concave and not even quasiconcave. In this note we show, for the centralize case, that the objective function is submodular, and partially verify Netessine and Rudi＇s observation that the objective function be unimodal in each of the decision variables for some case.展开更多
The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of (maximal) single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that...The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of (maximal) single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that mixed search number is equivalent to linear-width. Hence, by combining those results, we obtain a proof of the equivalence between linear tangle and maximal single ideal. This short report gives an alternative proof of the equivalence.展开更多
Submodular maximization is a significant area of interest in combinatorial optimization.It has various real-world applications.In recent years,streaming algorithms for submodular maximization have gained attention,all...Submodular maximization is a significant area of interest in combinatorial optimization.It has various real-world applications.In recent years,streaming algorithms for submodular maximization have gained attention,allowing realtime processing of large data sets by examining each piece of data only once.However,most of the current state-of-the-art algorithms are only applicable to monotone submodular maximization.There are still significant gaps in the approximation ratios between monotone and non-monotone objective functions.In this paper,we propose a streaming algorithm framework for non-monotone submodular maximization and use this framework to design deterministic streaming algorithms for the d-knapsack constraint and the knapsack constraint.Our 1-pass streaming algorithm for the d-knapsack constraint has a 1/4(d+1)-∈approximation ratio,using O(BlogB/∈)memory,and O(logB/∈)query time per element,where B=MIN(n,b)is the maximum number of elements that the knapsack can store.As a special case of the d-knapsack constraint,we have the 1-pass streaming algorithm with a 1/8-∈approximation ratio to the knapsack constraint.To our knowledge,there is currently no streaming algorithm for this constraint when the objective function is non-monotone,even when d=1.In addition,we propose a multi-pass streaming algorithm with 1/6-∈approximation,which stores O(B)elements.展开更多
Wireless Power Transmission(WPT)has been widely used to replenish energy for various rechargeable devices.The ElectroMagnetic Radiation(EMR)of WPT has attracted great attention of safety concerns.It is possible for th...Wireless Power Transmission(WPT)has been widely used to replenish energy for various rechargeable devices.The ElectroMagnetic Radiation(EMR)of WPT has attracted great attention of safety concerns.It is possible for the malicious attacker to launch the EMR attack by capturing multiple wireless chargers.Little work has studied the EMR attack itself.In this paper,we propose a realistic EMR hazard model,which outputs the diminishing marginal hazard with EMR,with adjustable parameters to the target entities.We formulate three EMR attack models,termed Cumulative EMR Attack(CEA),Overall EMR Attack(OEA)and Unsafety EMR Attack(UEA),and propose the performance guaranteed algorithm of EMR attack for each model.We conduct extensive simulations and field experiments on a testbed.The results show that the proposed algorithms can output the near-optimal solution with much less running time than the optimal algorithms.The results of field experiments in a small testbed show that the utilities of CEAA and OEAA are increased by 70.5%and 12.9%than the comparison algorithms,respectively.Moreover,the number of captured chargers of UEAA is 5.9%less than the comparison algorithms.Our simulations also show the designed algorithms can perform better in a large-scale charging network.展开更多
In this work,we study a k-Cardinality Constrained Regularized Submodular Maximization(k-CCRSM)problem,in which the objective utility is expressed as the difference between a non-negative submodular and a modular funct...In this work,we study a k-Cardinality Constrained Regularized Submodular Maximization(k-CCRSM)problem,in which the objective utility is expressed as the difference between a non-negative submodular and a modular function.No multiplicative approximation algorithm exists for the regularized model,and most works have focused on designing weak approximation algorithms for this problem.In this study,we consider the k-CCRSM problem in a streaming fashion,wherein the elements are assumed to be visited individually and cannot be entirely stored in memory.We propose two multipass streaming algorithms with theoretical guarantees for the above problem,wherein submodular terms are monotonic and nonmonotonic.展开更多
We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation ...We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy algorithm.For a streaming model,we propose a one-pass streaming algorithm.We also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular function.The total curvature is computable in polynomial time and widely utilized in the literature.展开更多
Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization.In this paper,we consider knapsack constraint.In this problem,we give n...Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization.In this paper,we consider knapsack constraint.In this problem,we give n articles and m categories,and the goal is to select a subset of articles that can maximize the function F(S).Function F(S)consists of m monotone submodular functions fj,j=1,2,…,m,and each fj measures the similarity of each article in category j.We present a constant-approximation algorithm for this problem.展开更多
In this paper,we investigate the maximization of the differences between a nonnegative monotone diminishing return submodular(DR-submodular)function and a nonnegative linear function on the integer lattice.As it is al...In this paper,we investigate the maximization of the differences between a nonnegative monotone diminishing return submodular(DR-submodular)function and a nonnegative linear function on the integer lattice.As it is almost unapproximable for maximizing a submodular function without the condition of nonnegative,we provide weak(bifactor)approximation algorithms for this problem in two online settings,respectively.For the unconstrained online model,we combine the ideas of single-threshold greedy,binary search and function scaling to give an efficient algorithm with a 1/2 weak approximation ratio.For the online streaming model subject to a cardinality constraint,we provide a one-pass(3-√5)/2 weak approximation ratio streaming algorithm.Its memory complexity is(k log k/ε),and the update time for per element is(log^(2)k/ε).展开更多
In this paper,we consider the parallel-machine customer order scheduling with delivery time and submodular rejection penalties.In this problem,we are given m dedicated machines in parallel and n customer orders.Each o...In this paper,we consider the parallel-machine customer order scheduling with delivery time and submodular rejection penalties.In this problem,we are given m dedicated machines in parallel and n customer orders.Each order has a delivery time and consists of m product types and each product type should be manufactured on a dedicated machine.An order is either rejected,in which case a rejection penalty has to be paid,or accepted and manufactured on the m dedicated machines.The objective is to find a solution to minimize the sum of the maximum delivery completion time of the accepted orders and the penalty of the rejected orders which is determined by a submodular function.We design an LP rounding algorithm with approximation ratio of n+1 for this problem.展开更多
In this paper,the structural properties of revenue management in a hubto-hub airline network is studied.Using a reformulated network flow version of the problem,it is shown that the optimal value has supermodularity,s...In this paper,the structural properties of revenue management in a hubto-hub airline network is studied.Using a reformulated network flow version of the problem,it is shown that the optimal value has supermodularity,submodularity,and Lconcavity in the network’s capacities dimensions.It is thus deduced that the certainty equivalent control thresholds used in the revenue management problem have monotone properties.These structural properties add important managerial insights into the network revenue management system.展开更多
It is shown that for a valid non-cooperative utility system,if the social utility function is submodular,then any Nash equilibrium achieves at least 1/2 of the optimal social utility,subject to a function-dependent ad...It is shown that for a valid non-cooperative utility system,if the social utility function is submodular,then any Nash equilibrium achieves at least 1/2 of the optimal social utility,subject to a function-dependent additive term.Moreover,if the social utility function is nondecreasing and submodular,then any Nash equilibrium achieves at least 1/(1+c)of the optimal social utility,where c is the curvature of the social utility function.In this paper,we consider variations of the utility system considered by Vetta,in which users are grouped together.Our aim is to establish how grouping and cooperation among users affect performance bounds.We consider two types of grouping.The first type is from a previous paper,where each user belongs to a group of users having social ties with it.For this type of utility system,each user’s strategy maximises its social group utility function,giving rise to the notion of social-aware Nash equilibrium.We prove that this social utility system yields to the bounding results of Vetta for non-cooperative system,thus establishing provable performance guarantees for the social-aware Nash equilibria.For the second type of grouping we consider,the set of users is partitioned into l disjoint groups,where the users within a group cooperate to maximise their group utility function,giving rise to the notion of group Nash equilibrium.In this case,each group can be viewed as a new user with vector-valued actions,and a 1/2 bound for the performance of group Nash equilibria follows from the result of Vetta.But as we show tighter bounds involving curvature can be established.By defining the group curvature cki associated with group i with ki users,we show that if the social utility function is nondecreasing and submodular,then any group Nash equilibrium achieves at least 1/(1+max1≤i≤l cki)of the optimal social utility,which is tighter than that for the case without grouping.As a special case,if each user has the same action space,then we have that any group Nash equilibrium achieves at least 1/(1+ck∗)of the optimal social utility,where k∗is the least number of users among the l groups.Finally,we present an example of a utility system for database-assisted spectrum access to illustrate our results.展开更多
The unified power flow controller(UPFC)based on modular multilevel converter(MMC) is the most creative flexible ac transmission system(FACTS) device. In theory, the output voltage of the series MMC in MMCUPFC can be r...The unified power flow controller(UPFC)based on modular multilevel converter(MMC) is the most creative flexible ac transmission system(FACTS) device. In theory, the output voltage of the series MMC in MMCUPFC can be regulated from 0 to the rated value. However,there would be relatively large harmonics in the output voltage if the voltage modulation ratio is small. In order to analyze the influence of MMC-UPFC on the harmonics of the power grid, the theoretical calculation method and spectra of the output voltage harmonics of MMC are presented. Subsequently, the calculation formulas of the harmonics in the power grid with UPFC are proposed. Based on it, the influence of UPFC on the grid voltage harmonics is evaluated, when MMC-UPFC is operated with different submodular numbers and voltage modular ratios. Eventually, the proposed analysis method is validated using digital simulation. The study results would provide guideline for the design and operation of MMC-UPFC project.展开更多
Social Influence Maximization Problems(SIMPs)deal with selecting k seeds in a given Online Social Network(OSN)to maximize the number of eventually-influenced users.This is done by using these seeds based on a given se...Social Influence Maximization Problems(SIMPs)deal with selecting k seeds in a given Online Social Network(OSN)to maximize the number of eventually-influenced users.This is done by using these seeds based on a given set of influence probabilities among neighbors in the OSN.Although the SIMP has been proved to be NP-hard,it has both submodular(with a natural diminishing-return)and monotone(with an increasing influenced users through propagation)that make the problem suitable for approximation solutions.However,several special SIMPs cannot be modeled as submodular or monotone functions.In this paper,we look at several conditions under which non-submodular or non-monotone functions can be handled or approximated.One is a profit-maximization SIMP where seed selection cost is included in the overall utility function,breaking the monotone property.The other is a crowd-influence SIMP where crowd influence exists in addition to individual influence,breaking the submodular property.We then review several new techniques and notions,including double-greedy algorithms and the supermodular degree,that can be used to address special SIMPs.Our main results show that for a specific SIMP model,special network structures of OSNs can help reduce its time complexity of the SIMP.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 61572135 and 61170085）, 973 project （2010CB328106）, Program for New Century Excellent Talents in China （NCET-10-0388）.
文摘The key issue in top-k retrieval, finding a set of k documents （from a large document collection） that can best answer a user＇s query, is to strike the optimal balance between relevance and diversity. In this paper, we study the top-k re- trieval problem in the framework of facility location analysis and prove he submodularity of that objective function which provides a theoretical approximation guarantee of factor 1 -1/ε for the （best-first） greedy search algorithm. Furthermore, we propose a two-stage hybrid search strategy which first ob- tains a high-quality initial set of top-k documents via greedy search, and then refines that result set iteratively via local search. Experiments on two large TREC benchmark datasets show that our two-stage hybrid search strategy approach can supersede the existing ones effectively and efficiently.
基金supported by Higher Educational Science and Technology Program of Shandong Province(No.J17KA171)Natural Science and Engineering Research Council of Canada(No.06446)+1 种基金the National Natural Science Foundation of China(No.11871081)Science and Technology Program of Beijing Education Commission(No.KM201810005006).
文摘In many kinds of games with economic significance,it is very important to study the submodularity of functions.In this paper,wemainly study the problem of maximizing a concave function over an intersection of two matroids.We obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some conditions.Moreover,we also present examples showing that these conditions can be satisfied.
文摘Alzheimer’s disease(AD)is a neurological disorder that predominantly affects the brain.In the coming years,it is expected to spread rapidly,with limited progress in diagnostic techniques.Various machine learning(ML)and artificial intelligence(AI)algorithms have been employed to detect AD using single-modality data.However,recent developments in ML have enabled the application of these methods to multiple data sources and input modalities for AD prediction.In this study,we developed a framework that utilizes multimodal data(tabular data,magnetic resonance imaging(MRI)images,and genetic information)to classify AD.As part of the pre-processing phase,we generated a knowledge graph from the tabular data and MRI images.We employed graph neural networks for knowledge graph creation,and region-based convolutional neural network approach for image-to-knowledge graph generation.Additionally,we integrated various explainable AI(XAI)techniques to interpret and elucidate the prediction outcomes derived from multimodal data.Layer-wise relevance propagation was used to explain the layer-wise outcomes in the MRI images.We also incorporated submodular pick local interpretable model-agnostic explanations to interpret the decision-making process based on the tabular data provided.Genetic expression values play a crucial role in AD analysis.We used a graphical gene tree to identify genes associated with the disease.Moreover,a dashboard was designed to display XAI outcomes,enabling experts and medical professionals to easily comprehend the predic-tion results.
基金This paper was supported by the National Natural Science Foundation of China (61562091), Natural Science Foundation of Yunnan Province (2014FA023,201501CF00022), Program for Innovative Research Team in Yunnan University (XT412011), and Program for Excellent Young Talents of Yunnan University (XT412003).
文摘Maximizing the spread of influence is to select a set of seeds with specified size to maximize the spread of influence under a certain diffusion model in a social network. In the actual spread process, the activated probability of node increases with its newly increasing activated neighbors, which also decreases with time. In this paper, we focus on the problem that selects k seeds based on the cascade model with diffusion decay to maximize the spread of influence in social networks. First, we extend the independent cascade model to incorporate the diffusion decay factor, called as the cascade model with diffusion decay and abbreviated as CMDD. Then, we discuss the objective function of maximizing the spread of influence under the CMDD, which is NP-hard. We further prove the monotonicity and submodularity of this objective function. Finally, we use the greedy algorithm to approximate the optimal result with the ration of 1 ? 1/e.
基金This paper was supported by the National Natural Science Foundation of China (61472345, 61562091), the Natural Science Foundation of Yunnan Province (2014FA023,2013FB010), the Program for Innovative Research Team in Yunnan University (XT412011), the Program for Excellent Young Talents of Yunnan University (XT412003), Yunnan Provincial Foundation for Leaders of Disciplines in Science and Technology (2012HB004), and the Research Foundation of the Educational Department of Yunnan Province (2014C134Y).
文摘There exist two or more competing products in viral marketing, and the companies can exploit the social interactions of users to propagate the awareness of products. In this paper, we focus on selecting seeds for maximizing the competitive influence spread in social networks. First, we establish the possible graphs based on the propagation probability of edges, and then we use the competitive influence spread model (CISM) to model the competitive spread under the possible graph. Further, we consider the objective function of selecting k seeds of one product under the CISM when the seeds of another product have been known, which is monotone and submodular, and thus we use the CELF (cost-effective lazy forward) algorithm to accelerate the greedy algorithm that can approximate the optimal with 1 ? 1/e. Experimental results verify the feasibility and effectiveness of our method.
基金supported by Natural Science Foundation of China under Grant No.91738202,91438206
文摘In remote terrestrial-satellite networks, caching is a very promising technique to alleviate the burden of space cloudlet(e.g., cache-enabled satellite user terminal) and to improve subscribers' quality of experience(Qo E) in terms of buffering delay and achievable video streaming rate. In this paper, we studied a Qo E-driven caching placement optimization problem for video streaming that takes into account the required video streaming rate and the social relationship among users. Social ties between users are used to designate a set of helpers with caching capability, which can cache popular files proactively when the cloudlet is idle. We model the utility function of Qo E as a logarithmic function. Then, the caching placement problem is formulated as an optimization problem to maximize the user's average Qo E subject to the storage capacity constraints of the helpers and the cloudlets. Furthermore, we reformulate the problem into a monotone submodular optimization problem with a partition matroid constraint, and an efficient greedy algorithm with 1-1 e approximation ratio is proposed to solve it. Simulation results show that the proposed caching placement approach significantly outperforms the traditional approaches in terms of Qo E, while yields about the same delay and hit ratio performance compare to the delay-minimized scheme.
文摘Netessine and Rudi（2003） consider a consumer-driven substitution problem with an arbitrary number of products under both centralized management and competition. They obtain analytically tractable solutions, establish concavity of the objective function, i.e., the expected profit function generated by each product and uniqueness of the equilibrium for the decentralize case. For the centralized case, they indicate that the objective function, i.e., the expected profit function, might not be concave and not even quasiconcave. In this note we show, for the centralize case, that the objective function is submodular, and partially verify Netessine and Rudi＇s observation that the objective function be unimodal in each of the decision variables for some case.
文摘The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of (maximal) single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that mixed search number is equivalent to linear-width. Hence, by combining those results, we obtain a proof of the equivalence between linear tangle and maximal single ideal. This short report gives an alternative proof of the equivalence.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.62325210 and 62272441).
文摘Submodular maximization is a significant area of interest in combinatorial optimization.It has various real-world applications.In recent years,streaming algorithms for submodular maximization have gained attention,allowing realtime processing of large data sets by examining each piece of data only once.However,most of the current state-of-the-art algorithms are only applicable to monotone submodular maximization.There are still significant gaps in the approximation ratios between monotone and non-monotone objective functions.In this paper,we propose a streaming algorithm framework for non-monotone submodular maximization and use this framework to design deterministic streaming algorithms for the d-knapsack constraint and the knapsack constraint.Our 1-pass streaming algorithm for the d-knapsack constraint has a 1/4(d+1)-∈approximation ratio,using O(BlogB/∈)memory,and O(logB/∈)query time per element,where B=MIN(n,b)is the maximum number of elements that the knapsack can store.As a special case of the d-knapsack constraint,we have the 1-pass streaming algorithm with a 1/8-∈approximation ratio to the knapsack constraint.To our knowledge,there is currently no streaming algorithm for this constraint when the objective function is non-monotone,even when d=1.In addition,we propose a multi-pass streaming algorithm with 1/6-∈approximation,which stores O(B)elements.
基金supported by National Natural Science Foundation of China(No.62372249,No.62072254)Jiangsu Graduate Scientific Research Innovation Program(No.KYCX210796).
文摘Wireless Power Transmission(WPT)has been widely used to replenish energy for various rechargeable devices.The ElectroMagnetic Radiation(EMR)of WPT has attracted great attention of safety concerns.It is possible for the malicious attacker to launch the EMR attack by capturing multiple wireless chargers.Little work has studied the EMR attack itself.In this paper,we propose a realistic EMR hazard model,which outputs the diminishing marginal hazard with EMR,with adjustable parameters to the target entities.We formulate three EMR attack models,termed Cumulative EMR Attack(CEA),Overall EMR Attack(OEA)and Unsafety EMR Attack(UEA),and propose the performance guaranteed algorithm of EMR attack for each model.We conduct extensive simulations and field experiments on a testbed.The results show that the proposed algorithms can output the near-optimal solution with much less running time than the optimal algorithms.The results of field experiments in a small testbed show that the utilities of CEAA and OEAA are increased by 70.5%and 12.9%than the comparison algorithms,respectively.Moreover,the number of captured chargers of UEAA is 5.9%less than the comparison algorithms.Our simulations also show the designed algorithms can perform better in a large-scale charging network.
基金This work was supported by the Beijing Natural Science Foundation Project(No.Z220004)the National Natural Science Foundation of China(Nos.11901544 and 12101587)the China Postdoctoral Science Foundation(No.2022M720329).
文摘In this work,we study a k-Cardinality Constrained Regularized Submodular Maximization(k-CCRSM)problem,in which the objective utility is expressed as the difference between a non-negative submodular and a modular function.No multiplicative approximation algorithm exists for the regularized model,and most works have focused on designing weak approximation algorithms for this problem.In this study,we consider the k-CCRSM problem in a streaming fashion,wherein the elements are assumed to be visited individually and cannot be entirely stored in memory.We propose two multipass streaming algorithms with theoretical guarantees for the above problem,wherein submodular terms are monotonic and nonmonotonic.
基金The first author was supported by the National Natural Science Foundation of China(Nos.12001025 and 12131003)The second author was supported by the Spark Fund of Beijing University of Technology(No.XH-2021-06-03)+2 种基金The third author was supported by the Natural Sciences and Engineering Research Council of Canada(No.283106)the Natural Science Foundation of China(Nos.11771386 and 11728104)The fourth author is supported by the National Natural Science Foundation of China(No.12001335).
文摘We investigate the problem of maximizing the sum of submodular and supermodular functions under a fairness constraint.This sum function is non-submodular in general.For an offline model,we introduce two approximation algorithms:A greedy algorithm and a threshold greedy algorithm.For a streaming model,we propose a one-pass streaming algorithm.We also analyze the approximation ratios of these algorithms,which all depend on the total curvature of the supermodular function.The total curvature is computable in polynomial time and widely utilized in the literature.
基金supported by the National Natural Science Foundation of China(Nos.12131003,12271259,11371001,11771386,and 11728104)the Natural Sciences and Engineering Research Council of Canada(NSERC)(No.06446)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20200267)Qinglan Project.
文摘Two-stage submodular maximization problem under cardinality constraint has been widely studied in machine learning and combinatorial optimization.In this paper,we consider knapsack constraint.In this problem,we give n articles and m categories,and the goal is to select a subset of articles that can maximize the function F(S).Function F(S)consists of m monotone submodular functions fj,j=1,2,…,m,and each fj measures the similarity of each article in category j.We present a constant-approximation algorithm for this problem.
基金supported by the National Natural Science Foundation of China(Nos.12001025 and 12131003)The second author is supported by the Natural Sciences and Engineering Research Council(No.06446),and the National Natural Science Foundation of China(Nos.11771386 and 11728104)+2 种基金The third author is supported by the National Natural Science Foundation of China(Nos.11501171 and 11771251)the Province Natural Science Foundation of Shandong(No.ZR2020MA028)The fourth author is supported by the National Natural Science Foundation of China(No.11701150)。
文摘In this paper,we investigate the maximization of the differences between a nonnegative monotone diminishing return submodular(DR-submodular)function and a nonnegative linear function on the integer lattice.As it is almost unapproximable for maximizing a submodular function without the condition of nonnegative,we provide weak(bifactor)approximation algorithms for this problem in two online settings,respectively.For the unconstrained online model,we combine the ideas of single-threshold greedy,binary search and function scaling to give an efficient algorithm with a 1/2 weak approximation ratio.For the online streaming model subject to a cardinality constraint,we provide a one-pass(3-√5)/2 weak approximation ratio streaming algorithm.Its memory complexity is(k log k/ε),and the update time for per element is(log^(2)k/ε).
基金the National Natural Science Foundation of China(No.11971146)the Natural Science Foundation of Hebei Province of China(Nos.A2019205089 and A2019205092)+1 种基金Hebei Province Foundation for Returnees(No.CL201714)the Graduate Innovation Grant Program of Hebei Normal University(No.CXZZSS2022053).
文摘In this paper,we consider the parallel-machine customer order scheduling with delivery time and submodular rejection penalties.In this problem,we are given m dedicated machines in parallel and n customer orders.Each order has a delivery time and consists of m product types and each product type should be manufactured on a dedicated machine.An order is either rejected,in which case a rejection penalty has to be paid,or accepted and manufactured on the m dedicated machines.The objective is to find a solution to minimize the sum of the maximum delivery completion time of the accepted orders and the penalty of the rejected orders which is determined by a submodular function.We design an LP rounding algorithm with approximation ratio of n+1 for this problem.
基金the Startup Grant of Scientific Research for Doctors of Luoyang Institute of Science and Technology,China(No.2011BZ12).
文摘In this paper,the structural properties of revenue management in a hubto-hub airline network is studied.Using a reformulated network flow version of the problem,it is shown that the optimal value has supermodularity,submodularity,and Lconcavity in the network’s capacities dimensions.It is thus deduced that the certainty equivalent control thresholds used in the revenue management problem have monotone properties.These structural properties add important managerial insights into the network revenue management system.
基金NSF and Division of Computing and Communication Foundations[grant number CCF-1422658]the CSU Information Science and Technology Center(ISTeC)。
文摘It is shown that for a valid non-cooperative utility system,if the social utility function is submodular,then any Nash equilibrium achieves at least 1/2 of the optimal social utility,subject to a function-dependent additive term.Moreover,if the social utility function is nondecreasing and submodular,then any Nash equilibrium achieves at least 1/(1+c)of the optimal social utility,where c is the curvature of the social utility function.In this paper,we consider variations of the utility system considered by Vetta,in which users are grouped together.Our aim is to establish how grouping and cooperation among users affect performance bounds.We consider two types of grouping.The first type is from a previous paper,where each user belongs to a group of users having social ties with it.For this type of utility system,each user’s strategy maximises its social group utility function,giving rise to the notion of social-aware Nash equilibrium.We prove that this social utility system yields to the bounding results of Vetta for non-cooperative system,thus establishing provable performance guarantees for the social-aware Nash equilibria.For the second type of grouping we consider,the set of users is partitioned into l disjoint groups,where the users within a group cooperate to maximise their group utility function,giving rise to the notion of group Nash equilibrium.In this case,each group can be viewed as a new user with vector-valued actions,and a 1/2 bound for the performance of group Nash equilibria follows from the result of Vetta.But as we show tighter bounds involving curvature can be established.By defining the group curvature cki associated with group i with ki users,we show that if the social utility function is nondecreasing and submodular,then any group Nash equilibrium achieves at least 1/(1+max1≤i≤l cki)of the optimal social utility,which is tighter than that for the case without grouping.As a special case,if each user has the same action space,then we have that any group Nash equilibrium achieves at least 1/(1+ck∗)of the optimal social utility,where k∗is the least number of users among the l groups.Finally,we present an example of a utility system for database-assisted spectrum access to illustrate our results.
基金supported by State Grid Corporation of China(SGCC)’s Major Science and Technology Demonstrative Project of UPFC in West Nanjing Power Grid(No.SGCC-2015-011)
文摘The unified power flow controller(UPFC)based on modular multilevel converter(MMC) is the most creative flexible ac transmission system(FACTS) device. In theory, the output voltage of the series MMC in MMCUPFC can be regulated from 0 to the rated value. However,there would be relatively large harmonics in the output voltage if the voltage modulation ratio is small. In order to analyze the influence of MMC-UPFC on the harmonics of the power grid, the theoretical calculation method and spectra of the output voltage harmonics of MMC are presented. Subsequently, the calculation formulas of the harmonics in the power grid with UPFC are proposed. Based on it, the influence of UPFC on the grid voltage harmonics is evaluated, when MMC-UPFC is operated with different submodular numbers and voltage modular ratios. Eventually, the proposed analysis method is validated using digital simulation. The study results would provide guideline for the design and operation of MMC-UPFC project.
基金the National Science Foundation(NSF)grants Computer and Network Systems(CNS)1824440,CNS 1828363,CNS 1757533,CNS 1618398,CNS 1651947,and CNS 1564128。
文摘Social Influence Maximization Problems(SIMPs)deal with selecting k seeds in a given Online Social Network(OSN)to maximize the number of eventually-influenced users.This is done by using these seeds based on a given set of influence probabilities among neighbors in the OSN.Although the SIMP has been proved to be NP-hard,it has both submodular(with a natural diminishing-return)and monotone(with an increasing influenced users through propagation)that make the problem suitable for approximation solutions.However,several special SIMPs cannot be modeled as submodular or monotone functions.In this paper,we look at several conditions under which non-submodular or non-monotone functions can be handled or approximated.One is a profit-maximization SIMP where seed selection cost is included in the overall utility function,breaking the monotone property.The other is a crowd-influence SIMP where crowd influence exists in addition to individual influence,breaking the submodular property.We then review several new techniques and notions,including double-greedy algorithms and the supermodular degree,that can be used to address special SIMPs.Our main results show that for a specific SIMP model,special network structures of OSNs can help reduce its time complexity of the SIMP.
