We give improved algorithms for constructing minimum directed and undirected cycle bases in graphs. For general graphs, the new algorithms are Monte Carlo and have running time O(m ω ), where ω is the exponent of matrix multiplication. The previous best algorithm had running time . For planar graphs, the new algorithm is deterministic and has running time O(n 2). The previous best algorithm had running time O(n 2 logn). A key ingredient to our improved running times is the insight that the search for minimum bases can be restricted to a set of candidate cycles of total length O(nm). © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Amaldi, E., Iuliano, C., Jurkiewicz, T., Mehlhorn, K., & Rizzi, R. (2009). Breaking the O(m 2 n) barrier for minimum cycle bases. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5757 LNCS, pp. 301–312). https://doi.org/10.1007/978-3-642-04128-0_28
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