Quantum Algorithm for Triangle Finding in Sparse Graphs
Algorithmica(2017)
摘要
This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. (SIAM J Comput 34(6):1324–1330, 2005 ). Our algorithm is based on the recent Õ(n^5/4) -query algorithm given by Le Gall (Proceedings of the 55th IEEE annual symposium on foundations of computer science, pp 216–225, 2014 ) for triangle finding over dense graphs (here n denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with O(n^5/4-ϵ) queries for some constant ϵ >0 whenever the graph has at most O(n^2-c) edges for some constant c>0 .
更多查看译文
关键词
Quantum algorithm,Quantum walk,Triangle finding
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络