Greedy Local Search and Vertex Cover in Sparse Random Graphs

(Extended Abstract)
  • Carsten Witt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


Recently, various randomized search heuristics have been studied for the solution of the minimum vertex cover problem, in particular for sparse random instances according to the G(n,c/n) model, where c > 0 is a constant. Methods from statistical physics suggest that the problem is easy if c < e. This work starts with a rigorous explanation for this claim based on the refined analysis of the Karp-Sipser algorithm by Aronson et al. Subsequently, theoretical supplements are given to experimental studies of search heuristics on random graphs. For c < 1, a greedy and randomized local-search heuristic finds an optimal cover in polynomial time with a probability arbitrarily close to 1. This behavior relies on the absence of a giant component. As an additional insight into the randomized search, it is shown that the heuristic fails badly also on graphs consisting of a single tree component of maximum degree 3.


Random Graph Vertex Cover Giant Component Optimal Cover Minimum Vertex Cover 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Carsten Witt
    • 1
  1. 1.DTU InformaticsTechnical University of DenmarkLyngbyDenmark

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