2011/05/31 by Gwenaël Joret, Christophe Paul, Ignasi Sau +2 · 13 citations
Computer Science · #Advanced Graph Theory Research #Approximation algorithm #Complexity and Algorithms in Graphs #Computational Geometry and Mesh Generation #Disjoint sets #Graph #Hypercube graph #Neighbourhood (mathematics) #Parameterized complexity #Path graph #Running time #Vertex (graph theory) #Vertex cover #acm:05C83 #acm:05C85 #cs.DS #msc:05C83 #msc:05C85
paper · pdf · doi:10.1137/120883736
published in SIAM Journal on Discrete Mathematics 28(3), 1363-1390 (Society for Industrial and Applied Mathematics) · v2: several minor changes
arxiv created 2013/12/13 · openalex publication_date 2014/01/01 · arxiv updated 2014/10/10 · openalex created_date 2017/05/26 · openalex updated_date 2026/08/05
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 hitting and packing c-pumpkin-models in a given graph in the realm of approximation algorithms and parameterized algorithms. We give a fixed-parameter tractable (FPT) algorithm running in time 2O(k) nO(1) deciding, for any fixed c ≥ 1, whether all c-pumpkin-models can be hit 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. Finally, we present an O(log n)-approximation algorithm for both the problems of hitting all c-pumpkin-models with a smallest number of vertices and packing a maximum number of vertex-disjoint c-pumpkin-models.