Paper Info
Title
A bottom-up method and fast algorithms for MAX INDEPENDENT SET
Abstract
We first propose a new method, called “bottom-up method”, that, informally, “propagates” improvement of the worst-case complexity for “sparse” instances to “denser” ones and we show an easy though non-trivial application of it to the min set cover problem. We then tackle max independent set. Following the bottom-up method we propagate improvements of worst-case complexity from graphs of average degree d to graphs of average degree greater than d. Indeed, using algorithms for max independent set in graphs of average degree 3, we tackle max independent set in graphs of average degree 4, 5 and 6. Then, we combine the bottom-up technique with measure and conquer techniques to get improved running times for graphs of maximum degree 4, 5 and 6 but also for general graphs. The best computation bounds obtained for max independent set are O*(1.1571n), O*(1.1918n) and O*(1.2071n), for graphs of maximum (or more generally average) degree 4, 5 and 6 respectively, and O*(1.2127n) for general graphs. These results improve upon the best known polynomial space results for these cases.
Year
DOI
Venue
2010
10.1007/978-3-642-13731-0_7
SWAT
Keywords
Field
DocType
bottom-up method,general graph,maximum degree,min set cover problem,average degree,worst-case complexity,max independent set,best computation,fast algorithm,new method,bottom-up technique,set covering problem,bottom up,independent set
Set cover problem,Discrete mathematics,Combinatorics,Indifference graph,Chordal graph,Algorithm,Hopcroft–Karp algorithm,PSPACE,Independent set,Degree (graph theory),Mathematics,Maximal independent set
Conference
Volume
ISSN
ISBN
6139
0302-9743
3-642-13730-X
Citations 
PageRank 
References 
3
0.40
8
Authors
4
Name
Order
Citations
PageRank
Nicolas Bourgeois1997.96
Bruno Escoffier243037.32
Vangelis Th. Paschos363363.97
Johan M. M. van Rooij419211.20