Domination in convex and chordal bipartite graphs
Information Processing Letters
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Linear time algorithms on circular-arc graphs
Information Processing Letters
The complexity of domination problems in circle graphs
Discrete Applied Mathematics
Independence and domination in polygon graphs
Discrete Applied Mathematics
Dominations in trapezoid graphs
Information Processing Letters
Efficient Algorithms for the Domination Problems on Interval and Circular-Arc Graphs
SIAM Journal on Computing
Graph classes: a survey
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An $O(N + M)$-Time Algorithm for Finding a Minimum-WeightDominating Set in a Permutation Graph
SIAM Journal on Computing
Branch-width and well-quasi-ordering in matroids and graphs
Journal of Combinatorial Theory Series B
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Generalized domination in chordal graphs
Nordic Journal of Computing
Weighted Domination on Cocomparability Graphs
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
H-Colorings of Large Degree Graphs
EurAsia-ICT '02 Proceedings of the First EurAsian Conference on Information and Communication Technology
On the Clique-Width of Perfect Graph Classes
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
On the restriction of some NP-complete graph problems to permutation graphs
FCT '85 Fundamentals of Computation Theory
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Parameterized and Exact Computation
The rank-width of the square grid
Discrete Applied Mathematics
Computing role assignments of chordal graphs
Theoretical Computer Science
On the Boolean-width of a graph: structure and applications
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Finding good decompositions for dynamic programming on dense graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Sitting closer to friends than enemies, revisited
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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Boolean-width is a recently introduced graph width parameter. If a boolean decomposition of width w is given, several NP-complete problems, such as Maximum Weight Independent Set, k-Coloring and Minimum Weight Dominating Set are solvable in O*(2O(w)) time [6]. In this paper we study graph classes for which we can compute a decomposition of logarithmic boolean-width in polynomial time. Since 2O(logn)=nO(1), this gives polynomial time algorithms for the above problems on these graph classes. For interval graphs we show how to construct decompositions where neighborhoods of vertex subsets are nested. We generalize this idea to neighborhoods that can be represented by a constant number of vertices. Moreover we show that these decompositions have boolean-width O(logn). Graph classes having such decompositions include circular arc graphs, circular k-trapezoid graphs, convex graphs, Dilworth k graphs, k-polygon graphs and complements of k-degenerate graphs. Combined with results in [1,5], this implies that a large class of vertex subset and vertex partitioning problems can be solved in polynomial time on these graph classes.