2006 2nd International Conference on Information &Amp; Communication Technologies
DOI: 10.1109/ictta.2006.1684854
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An Improved Exact Algorithm for the Domatic Number Problem

Abstract: The 3-domatic number problem asks whether a given graph can be partitioned into three dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695 n (up to polynomial factors). This result improves the previous bound of 2.8805 n , which is due to Fomin, Grandoni, Pyatkin, and Stepanov. To prove our result, we combine an algorithm by Fomin et al. with Yamamoto's algorithm for the satisfiability problem. In addition, we show that the 3-domatic number problem can be solved … Show more

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Cited by 5 publications
(5 citation statements)
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“…Fomin et al [20] provided an O(2.8718 n ) time algorithm for deciding the domatic number, and Riege et al [40] presented an O(2.6949 n ) time, polynomial space algorithm for deciding if the domatic number is at least three. No prior nontrivial polynomial space algorithm for the general problem is known to the authors.…”
Section: Previous Work and Discussionmentioning
confidence: 99%
“…Fomin et al [20] provided an O(2.8718 n ) time algorithm for deciding the domatic number, and Riege et al [40] presented an O(2.6949 n ) time, polynomial space algorithm for deciding if the domatic number is at least three. No prior nontrivial polynomial space algorithm for the general problem is known to the authors.…”
Section: Previous Work and Discussionmentioning
confidence: 99%
“…Fomin et al [13] give an O * (2.8805 n ) algorithm for finding the domatic number; Riege et al [26] give an O * (2.695 n ) algorithm for the three domatic number problem. For graph coloring Björklund and Husfeldt [6] give an O * (2.3236 n ) algorithm; remarkably, this algorithm is based on the inclusion-exclusion principle.…”
Section: Previous Researchmentioning
confidence: 99%
“…In [17], Poon, Yen and Ung proved that finding a domatic partition into 3 dominating sets is NP-complete on planar bipartite graphs, and finding a domatic partition with d(G) elements in co-bipartite graphs is NP-complete. In [18], Riege, Rothe, Spakowski and Yamamoto showed that, given an arbitrary graph G, it is possible to determine if V (G) can be partitioned into 3 disjoint dominating sets with a deterministic algorithm in time 2.695 n (up to polynomial factors) and in polynomial space. Domatic partitions in graphs have been studied for some researches due its applications and theoretical results (see [9], [10], [12] [16] [17], [18]).…”
Section: Introductionmentioning
confidence: 99%
“…In [18], Riege, Rothe, Spakowski and Yamamoto showed that, given an arbitrary graph G, it is possible to determine if V (G) can be partitioned into 3 disjoint dominating sets with a deterministic algorithm in time 2.695 n (up to polynomial factors) and in polynomial space. Domatic partitions in graphs have been studied for some researches due its applications and theoretical results (see [9], [10], [12] [16] [17], [18]). Due a large amount of kinds of dominating sets (see [13] and [14]), several authors defined variants on the domatic number in graphs, for instance, total domatic number (Cockayne, Hedetniemi and Dawes [7]), idomatic number (Cockayne and Hedetniemi [8]), k-domatic number (Zelinka [20]) and tree domatic number (Chen [4]).…”
Section: Introductionmentioning
confidence: 99%