Publication: Research - peer-review › Journal article – Annual report year: 2012
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. (1998) . Subsequently, theoretical supplements are given to experimental studies of search heuristics on random graphs. For c<1, an iterated 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.
|Journal||Theoretical Computer Science|
This article is published in: "Special Issue on Theoretical Foundations of Evolutionary Computation" in the journal: "Theoretical Computer Science"
|Citations||Web of Science® Times Cited: 1|
- Randomized search heuristics, Iterated local search, Vertex cover, Random graphs, Karp–Sipser algorithm, e-phenonemon