We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our const...We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our construction has a natural generalization to the larger class of chordal graphs.This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.展开更多
Fast identifying the amount of information that can be gained by measuring a network via shortest-paths is one of the fundamental problem for networks exploration and monitoring.However,the existing methods are time-c...Fast identifying the amount of information that can be gained by measuring a network via shortest-paths is one of the fundamental problem for networks exploration and monitoring.However,the existing methods are time-consuming for even moderate-scale networks.In this paper,we present a method for fast shortest-path cover identification in both exact and approximate scenarios based on the relationship between the identification and the shortest distance queries.The effectiveness of the proposed method is validated through synthetic and real-world networks.The experimental results show that our method is 105 times faster than the existing methods and can solve the shortest-path cover identification in a few seconds for large-scale networks with millions of nodes and edges.展开更多
文摘We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our construction has a natural generalization to the larger class of chordal graphs.This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.
基金This work was supported in part by the National Natural Science Foundation of China(61471101)the National Natural Science Foundation of China(U1736205).
文摘Fast identifying the amount of information that can be gained by measuring a network via shortest-paths is one of the fundamental problem for networks exploration and monitoring.However,the existing methods are time-consuming for even moderate-scale networks.In this paper,we present a method for fast shortest-path cover identification in both exact and approximate scenarios based on the relationship between the identification and the shortest distance queries.The effectiveness of the proposed method is validated through synthetic and real-world networks.The experimental results show that our method is 105 times faster than the existing methods and can solve the shortest-path cover identification in a few seconds for large-scale networks with millions of nodes and edges.
