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Conference Papers Year : 2011

Hitting and Harvesting Pumpkins


The c-pumpkin is the graph with two vertices linked by c ≥ 1 parallel edges. A c-pumpkin-model in a graph G is a pair {A, B} of disjoint subsets of vertices of G, each inducing a connected subgraph of G, such that there are at least c edges in G between A and B. We focus on covering and packing c-pumpkin-models in a given graph: On the one hand, we provide an FPT algorithm running in time 2^{O(k)}.n^{O(1)} deciding, for any fixed c ≥ 1, whether all c-pumpkin-models can be covered by at most k vertices. This generalizes known single-exponential FPT algorithms for Vertex Cover and Feedback Vertex Set, which correspond to the cases c = 1, 2 respectively. On the other hand, we present a O(log n)-approximation algorithm for both the problems of covering all c-pumpkin-models with a smallest number of vertices, and packing a maximum number of vertex-disjoint c-pumpkin-models.

Dates and versions

lirmm-00642341 , version 1 (17-11-2011)



Gwénaël Joret, Christophe Paul, Ignasi Sau, Saket Saurabh, Stéphan Thomassé. Hitting and Harvesting Pumpkins. ESA 2011 - 19th Annual European Symposium on Algorithms, Sep 2011, Saarbrücken, Germany. pp.394-407, ⟨10.1007/978-3-642-23719-5_34⟩. ⟨lirmm-00642341⟩
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