A Bottom-Up Method and Fast Algorithms for max independent set
Bourgeois, Nicolas; Escoffier, Bruno; Paschos, Vangelis (2010), A Bottom-Up Method and Fast Algorithms for max independent set, in Kaplan, Haim, 12th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings, Springer : Berlin, p. 62-73
TypeCommunication / Conférence
Conference title12th Scandinavian Symposium and Workshops on Algorithm Theory - SWAT'10
Book title12th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings
Book authorKaplan, Haim
Series titleLecture Notes in Computer Science
Number of pages450
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Abstract (EN)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 *(1.1571 n ), O *(1.1918 n ) and O *(1.2071 n ), for graphs of maximum (or more generally average) degree 4, 5 and 6 respectively, and O *(1.2127 n ) for general graphs. These results improve upon the best known polynomial space results for these cases.
Subjects / KeywordsExact Algorithms; Max Independent Set; Bottom-Up Method
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Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms Bourgeois, Nicolas; Escoffier, Bruno; Paschos, Vangelis (2011) Article accepté pour publication ou publié