Combinatorial Dominance Guarantees for Heuristic Algorithms - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2007

Combinatorial Dominance Guarantees for Heuristic Algorithms


An $f(n)$ $\textit{dominance bound}$ on a heuristic for some problem is a guarantee that the heuristic always returns a solution not worse than at least $f(n)$ solutions. In this paper, we analyze several heuristics for $\textit{Vertex Cover}$, $\textit{Set Cover}$, and $\textit{Knapsack}$ for dominance bounds. In particular, we show that the well-known $\textit{maximal matching}$ heuristic of $\textit{Vertex Cover}$ provides an excellent dominance bound. We introduce new general analysis techniques which apply to a wide range of problems and heuristics for this measure. Certain general results relating approximation ratio and combinatorial dominance guarantees for optimization problems over subsets are established. We prove certain limitations on the combinatorial dominance guarantees of polynomial-time approximation schemes (PTAS), and give inapproximability results for the problems above.
Fichier principal
Vignette du fichier
dmAH0106.pdf (242.69 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01184785 , version 1 (17-08-2015)



Daniel Berend, Steven S. Skiena, Yochai Twitto. Combinatorial Dominance Guarantees for Heuristic Algorithms. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.79-94, ⟨10.46298/dmtcs.3537⟩. ⟨hal-01184785⟩


219 View
487 Download



Gmail Facebook Twitter LinkedIn More