TY - GEN

T1 - Upper bounds on boolean-width with applications to exact algorithms

AU - Rabinovich, Yuri

AU - Telle, Jan Arne

AU - Vatshelle, Martin

PY - 2013

Y1 - 2013

N2 - Boolean-width is similar to clique-width, rank-width and NLC-width in that all these graph parameters are constantly bounded on the same classes of graphs. In many classes where these parameters are not constantly bounded, boolean-width is distinguished by its much lower value, such as in permutation graphs and interval graphs where boolean-width was shown to be O(log n) [1]. Together with FPT algorithms having runtime O*(cboolw) for a constant c this helped explain why a variety of problems could be solved in polynomial-time on these graph classes. In this paper we continue this line of research and establish non-trivial upper-bounds on the boolean-width and linear boolean-width of any graph. Again we combine these bounds with FPT algorithms having runtime O*(cboolw), now to give a common framework of moderately-exponential exact algorithms that beat brute-force search for several independence and domination-type problems, on general graphs. Boolean-width is closely related to the number of maximal independent sets in bipartite graphs. Our main result breaking the triviality bound of n/3 for boolean-width and n/2 for linear boolean-width is proved by new techniques for bounding the number of maximal independent sets in bipartite graphs.

AB - Boolean-width is similar to clique-width, rank-width and NLC-width in that all these graph parameters are constantly bounded on the same classes of graphs. In many classes where these parameters are not constantly bounded, boolean-width is distinguished by its much lower value, such as in permutation graphs and interval graphs where boolean-width was shown to be O(log n) [1]. Together with FPT algorithms having runtime O*(cboolw) for a constant c this helped explain why a variety of problems could be solved in polynomial-time on these graph classes. In this paper we continue this line of research and establish non-trivial upper-bounds on the boolean-width and linear boolean-width of any graph. Again we combine these bounds with FPT algorithms having runtime O*(cboolw), now to give a common framework of moderately-exponential exact algorithms that beat brute-force search for several independence and domination-type problems, on general graphs. Boolean-width is closely related to the number of maximal independent sets in bipartite graphs. Our main result breaking the triviality bound of n/3 for boolean-width and n/2 for linear boolean-width is proved by new techniques for bounding the number of maximal independent sets in bipartite graphs.

UR - http://www.scopus.com/inward/record.url?scp=84893083691&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-03898-8_26

DO - 10.1007/978-3-319-03898-8_26

M3 - Conference contribution

AN - SCOPUS:84893083691

SN - 9783319038971

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 308

EP - 320

BT - Parameterized and Exact Computation - 8th International Symposium, IPEC 2013, Revised Selected Papers

T2 - 8th International Symposium on Parameterized and Exact Computation, IPEC 2013

Y2 - 4 September 2013 through 6 September 2013

ER -