Hitting and Harvesting Pumpkins
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Publication:5892008
DOI10.1137/120883736zbMATH Open1305.05221arXiv1105.2704OpenAlexW3100974949MaRDI QIDQ5892008
Author name not available (Why is that?)
Publication date: 22 December 2014
Published in: (Search for Journal in Brave)
Abstract: The "c-pumpkin" is the graph with two vertices linked by c>0 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>0, 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.
Full work available at URL: https://arxiv.org/abs/1105.2704
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