1994 | ReviewPaper | Buchkapitel
Improved approximations of independent sets in bounded-degree graphs
verfasst von : Magnús M. Halldórsson, Jaikumar Radhakrishnan
Erschienen in: Algorithm Theory — SWAT '94
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Finding maximum independent sets in graphs with bounded maximum degree is a well-studied NP-complete problem. We study two approaches for finding approximate solutions, and obtain several improved performance ratios.The first is a subgraph removal schema introduced in our previous paper. Using better component algorithms, we obtain an efficient method with a Δ/6(1+o(1)) performance ratio. We then produce an implementation of a theorem of Ajtai et al. on the independence number of clique-free graphs, and use it to obtain a O(Δ/loglogΔ) performance ratio with our schema. This is the first o(Δ) ratio.The second is a local search method of Berman and Fürer for which they proved a fine performance ratio but by using extreme amounts of time. We show how to substantially decrease the computing requirements while maintaining the same performance ratios of roughly (Δ+3)/5 for graphs with maximum degree Δ. We then show that a scaled-down version of their algorithm yields a (Δ+3)/4 performance, improving on previous bounds for reasonably efficient methods.