Efficient Enumeration Algorithms for Connected Induced Subgraphs with Large Girth
نویسندگان
چکیده
The girth is the length of shortest cycle in a graph. Recently, the problem for computing the girth of a graph have been studied well. Itai and Rodeh developed the first non trivial algorithm for computing girth in general graphs. Their algorithm runs in O (nm) time in the worst case and it runs in O(n) time on average case. For unweighted planer graphs, Djidjev gave a O ( n log n ) time algorithm for computing girth. Chang et al. improved Djidjev’s algorithm to a linear time algorithm. To the best of our knowledge. there are no known results for enumeration of induced connected subgraphs with large girth. In this paper, we propose two algorithms to solve this problem. The former algorithm enumerates all solutions in O (n) time using O ( n ) space. The latter algorithm enumerates all solutions in O (m) time using O (m) space.
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