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- W2104534750 abstract "In this paper, we consider the problem of computing a minimum cycle basis of an undirected graph G = ( V , E ) with n vertices and m edges. We describe an efficient implementation of an O ( m 3 + mn 2 log n ) algorithm. For sparse graphs, this is the currently best-known algorithm. This algorithm's running time can be partitioned into two parts with time O ( m 3 ) and O ( m 2 n + mn 2 log n ), respectively. Our experimental findings imply that for random graphs the true bottleneck of a sophisticated implementation is the O ( m 2 n + mn 2 log n ) part. A straightforward implementation would require Ω( nm ) shortest-path computations. Thus, we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speed-up. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis to obtain a new hybrid algorithm with running time O ( m 2 n 2 ). The hybrid algorithm is very efficient, in practice, for random dense unweighted graphs. Finally, we compare these two algorithms with a number of previous implementations for finding a minimum cycle basis of an undirected graph." @default.
- W2104534750 created "2016-06-24" @default.
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- W2104534750 date "2007-02-09" @default.
- W2104534750 modified "2023-09-26" @default.
- W2104534750 title "Implementing minimum cycle basis algorithms" @default.
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- W2104534750 doi "https://doi.org/10.1145/1187436.1216582" @default.
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