Finding Cycles and Trees in Sublinear Time

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least k 3 and tree-minors in bounded-degree graphs. The complexity of these algorithms is related to the distance of the graph from being Ck-minor free (resp., free from having the corresponding tree-minor). In particular, if the graph is (1)-far from being cycle-free (i.e., a constant fraction of the edges must be deleted to make the graph cycle-free), then the algorithm finds a cycle of polylogarithmic length in time O( N), where N denotes the number of vertices. This time complexity is optimal up to polylogarithmic factors. The foregoing results are the outcome of our study of the complexity of one-sided error property testing algorithms in the bounded-degree graphs model. For example, we show that cycle-freeness of N-vertex graphs can be tested with one-sided error within time complexity O(poly(1/)

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Artur Czumaj, Oded Goldreich, Dana Ron, C. Seshadhri, Asaf Shapira, Christian Sohler
• Keywords: Algorithm, CORR 2010, Education, One-sided Error, Time Complexity