Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Theoretical Computer Science
A better list heuristic for vertex cover
Information Processing Letters
A list heuristic for vertex cover
Operations Research Letters
Analytical and experimental comparison of six algorithms for the vertex cover problem
Journal of Experimental Algorithmics (JEA)
Hi-index | 0.89 |
In 2005, Demange and Paschos proposed in [M. Demange, V.Th. Paschos, On-line vertex-covering, Theoret. Comput. Sci. 332 (2005) 83-108] an online algorithm (noted LR here) for the classical vertex cover problem. They shown that, for any graph of maximum degree @D, LR constructs a vertex cover whose size is at most @D times the optimal one (this bound is tight in the worst case). Very recently, two of the present authors have shown in [F. Delbot, C. Laforest, A better list heuristic for vertex cover, Inform. Process. Lett. 107 (2008) 125-127] that LR has interesting properties (it is a good ''list algorithm'' and it can easily be distributed). In addition, LR has good experimental behavior in spite of its @D approximation (or competitive) ratio and the fact that it can be executed without the knowledge of the full instance at the beginning. In this paper we analyze it deeper and we show that LR has good ''average'' performances: we prove that its mean approximation ratio is strictly less than 2 for any graph and is equal to 1+e^-^2~1.13 in paths. LR is then a very interesting algorithm for constructing small vertex covers, despite its bad worst case behavior.