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Packing Short Cycles

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Cycle packing problems address minimizing path lengths in weighted graphs, revealing complexity and tractability implications.

An algorithm for Min-Sum Cycle Packing finds the minimum weight of vertex-disjoint cycles in polynomial time.
W[1]-hardness of Min-Sum Cycle Packing parameterized by k impacts its computational feasibility in graphs.
Shortest Cycle Packing is provably fixed-parameter tractable in weighted planar graphs, demonstrating potential efficiency.
A polynomial kernel for the edge-disjoint variant on planar graphs highlights the complexity of these problems.

Bentert et al. (2025) studied this question.

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