TY - GEN
T1 - Greedy Local Search and Vertex Cover in Sparse Random Graphs
AU - Witt, Carsten
N1 - Extended abstract.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-642-02017-9_43
DO - 10.1007/978-3-642-02017-9_43
M3 - Article in proceedings
SN - 978-3-642-02016-2
T3 - Lecture Notes in Computer Science
SP - 410
EP - 419
BT - Theory and Applications of Models of Computation
PB - Springer
T2 - 6th Annual Conference on Theory and Applications of Models of Computation (TAMC 2009)
Y2 - 18 May 2009 through 22 May 2009
ER -