A faster algorithm for computing the girth of planar and bounded genus graphs
ACM Transactions on Algorithms(2010)
摘要
The girth of a graph G is the length of a shortest cycle of G. In this article we design an O(n5/4 log n) algorithm for finding the girth of an undirected n-vertex planar graph, the first o(n2) algorithm for this problem. We also extend our results for the class of graphs embedded into an orientable surface of small genus. Our approach uses several techniques such as graph partitioning, hammock decomposition, graph covering, and dynamic shortest-path computation. We discuss extensions and generalizations of our result.
更多查看译文
关键词
cycles,undirected n-vertex planar graph,shortest cycle,girth,planar graphs,hammock decomposition,path and circuit problems,log n,dynamic shortest-path computation,dynamic algorithms,orientable surface,graph algorithms,small genus,shortest paths,graph separators,graph partitioning,graph g,graph genus,graphs,bounded genus graph,faster algorithm,shortest path,graph embedding,planar graph
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络