Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bol...Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/3？ We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes.In particular, it is shown that any graph G with m edges has a partition V_1,..., V_k such that each vertex set meets at least（1-（1-1/k）~2）m ＋ o（m） edges, which answers a related question of Bollobás and Scott.展开更多
The rapid growth of marine applications leads to a significant increase in Maritime Devices(MDs).Traditional shore-based maritime communication networks face limitations,such as overloaded and transmission distance to...The rapid growth of marine applications leads to a significant increase in Maritime Devices(MDs).Traditional shore-based maritime communication networks face limitations,such as overloaded and transmission distance to provide network services for MDs.Unmanned Aerial Vehicles(UAVs)act as relays that can expand coverage and enhance the quality of service for offshore communication networks.We consider a multi-UAV-assisted Offshore Internet of Things(mUAV-OloT),and formulate a throughput maximization problem by jointly optimizing channel allocation,Leader MD(LMD)selection,UAV-LMD association,and LMD-MD association.Firstly,we propose the Hypergraph-based Two-Stage Matching(HTSM)algorithm where a Hypergraph-based LMD Selection(HLMDS)strategy is employed to identify the set of LMDs.Secondly,the Kuhn-Munkres algorithm is used to optimize the UAV-LMD association and a Weighted Threedimensional Hypergraph Matching(WTHM)algorithm is designed to solve the LMD-MD association and channel allocation.Numerical results show that the HTSM algorithm outperforms benchmark algorithms regarding throughput.展开更多
基金National Natural Science Foundation of China (Grant Nos. 11371355 and 11471193)
文摘Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/3？ We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes.In particular, it is shown that any graph G with m edges has a partition V_1,..., V_k such that each vertex set meets at least（1-（1-1/k）~2）m ＋ o（m） edges, which answers a related question of Bollobás and Scott.
基金supported by the National Natural Science Foundation of China(Nos.51939001,62371085,62122069,and 62071431)the Fundamental Research Funds for the Central Universities(No.3132023514)the FDCT-MOST Joint Project(No.0066/2019/AMJ).
文摘The rapid growth of marine applications leads to a significant increase in Maritime Devices(MDs).Traditional shore-based maritime communication networks face limitations,such as overloaded and transmission distance to provide network services for MDs.Unmanned Aerial Vehicles(UAVs)act as relays that can expand coverage and enhance the quality of service for offshore communication networks.We consider a multi-UAV-assisted Offshore Internet of Things(mUAV-OloT),and formulate a throughput maximization problem by jointly optimizing channel allocation,Leader MD(LMD)selection,UAV-LMD association,and LMD-MD association.Firstly,we propose the Hypergraph-based Two-Stage Matching(HTSM)algorithm where a Hypergraph-based LMD Selection(HLMDS)strategy is employed to identify the set of LMDs.Secondly,the Kuhn-Munkres algorithm is used to optimize the UAV-LMD association and a Weighted Threedimensional Hypergraph Matching(WTHM)algorithm is designed to solve the LMD-MD association and channel allocation.Numerical results show that the HTSM algorithm outperforms benchmark algorithms regarding throughput.
