Minimum Cycle Bases of Weighted Outerplanar Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Minimum cycle bases of weighted outerplanar graphs
Information Processing Letters
Properties of Gomory-Hu co-cycle bases
Theoretical Computer Science
A polynomial time algorithm for minimum cycle basis in directed graphs
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Efficient deterministic algorithms for finding a minimum cycle basis in undirected graphs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
Approximating the diameter of planar graphs in near linear time
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The all-pairs min cut (APMC) problem on a normegative weighted graph is the problem of finding, for every pair of nodes, the min cut separating the pair. It is shown that on planar graphs, the APMC problem is equivalent to another problem, the minimum cycle basis (MCB) problem, on the dual graph. This is shown by characterizing the structure of MCBs on planar graphs in several ways. This leads to a new algorithm for solving both of these problems on planar graphs. The complexity of this algorithm equals that of the best algorithm for either problem, but is simpler.