-
[show abstract]
[hide abstract]
ABSTRACT: In the study of full bubble model graphs of bounded clique-width and bounded
linear clique-width, we determined complete sets of forbidden induced
subgraphs, that are minimal in the class of full bubble model graphs. In this
note, we show that (almost all of) these graphs are minimal in the class of all
graphs. As a corollary, we can give sets of minimal forbidden induced subgraphs
for graphs of bounded clique-width and for graphs of bounded linear
clique-width for arbitrary bounds.
06/2013;
-
Theor. Comput. Sci. 01/2011; 412:7001-7008.
-
Theor. Comput. Sci. 01/2011; 412:5466-5486.
-
Theor. Comput. Sci. 01/2011; 412:1275-1297.
-
Computer Science - Theory and Applications - 6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Proceedings; 01/2011
-
Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Dallas, TX, USA, August 14-16, 2011. Proceedings; 01/2011
-
Inf. Process. Lett. 01/2010; 110:312-316.
-
Theory and Applications of Models of Computation, 7th Annual Conference, TAMC 2010, Prague, Czech Republic, June 7-11, 2010. Proceedings; 01/2010
-
Algorithms and Computation - 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part II; 01/2010
-
[show abstract]
[hide abstract]
ABSTRACT: We study the classical Bandwidth problem from the viewpoint of parameterized algorithms. In the Bandwidth problem we are given a graph G = (V,E) together with a positive integer k, and asked whether there is an bijective function β: {1, ..., n} →V such that for every edge uv ∈ E, |β
− 1(u) − β
− 1(v)| ≤ k. The problem is notoriously hard, and it is known to be NP-complete even on very restricted subclasses of trees. The best known algorithm for Bandwidth for small values of k is the celebrated algorithm by Saxe[SIAM Journal on Algebraic and Discrete Methods, 1980 ], which runs in time 2O(k)nk+12^{{\mathcal{O}}(k)}n^{k+1}. In a seminal paper, Bodlaender, Fellows and Hallet[STOC 1994 ] ruled out the existence of an algorithm with running time of the form f(k)nO(1)f(k)n^{{\mathcal{O}}(1)} for any function f even for trees, unless the entire W-hierarchy collapses.
We initiate the search for classes of graphs where Bandwidth is fixed parameter tractable (FPT), that is, solvable in time f(k)nO(1)f(k)n^{{\mathcal{O}}(1)} for some function f. In this paper we present an algorithm with running time 2O(k logk) n22^{{\mathcal O}(k \log k)} n^2 for Bandwidth on AT-free graphs, a well-studied graph class that contains interval, permutation, and cocomparability graphs. Our result
is the first non-trivial FPT algorithm for Bandwidth on a graph class where the problem remains NP-complete.
12/2009: pages 573-582;
-
[show abstract]
[hide abstract]
ABSTRACT: Polar graphs generalise bipartite, cobipartite, split graphs, and they constitute a special type of matrix partitions. A graph
is polar if its vertex set can be partitioned into two, such that one part induces a complete multipartite graph and the other
part induces a disjoint union of complete graphs. Deciding whether a given arbitrary graph is polar, is an NP-complete problem.
Here we show that for permutation graphs this problem can be solved in polynomial time. The result is surprising, as related
problems like achromatic number and cochromatic number are NP-complete on permutation graphs. We give a polynomial-time algorithm
for recognising graphs that are both permutation and polar. Prior to our result, polarity has been resolved only for chordal
graphs and cographs.
11/2009: pages 218-229;
-
Electronic Notes in Discrete Mathematics. 01/2009; 32:27-34.
-
Combinatorial Algorithms, 20th International Workshop, IWOCA 2009, Hradec nad Moravicí, Czech Republic, June 28-July 2, 2009, Revised Selected Papers; 01/2009
-
J. Discrete Algorithms. 01/2009; 7:533-544.
-
Theory and Applications of Models of Computation, 6th Annual Conference, TAMC 2009, Changsha, China, May 18-22, 2009. Proceedings; 01/2009
-
Algorithms and Computation, 20th International Symposium, ISAAC 2009, Honolulu, Hawaii, USA, December 16-18, 2009. Proceedings; 01/2009
-
[show abstract]
[hide abstract]
ABSTRACT: The problem of computing minimum distortion embeddings of a given graph into a line (path) was introduced in 2004 and has
quickly attracted significant attention with subsequent results appearing in recent stoc and soda conferences. So far all such results concern approximation algorithms or exponential-time exact algorithms. We give the first
polynomial-time algorithms for computing minimum distortion embeddings of graphs into a path when the input graphs belong
to specific graph classes. In particular, we solve this problem in polynomial time for bipartite permutation graphs and threshold
graphs.
07/2008: pages 331-342;
-
Theory and Applications of Models of Computation, 5th International Conference, TAMC 2008, Xi'an, China, April 25-29, 2008. Proceedings; 01/2008
-
LATIN 2008: Theoretical Informatics, 8th Latin American Symposium, Búzios, Brazil, April 7-11, 2008, Proceedings; 01/2008
-
Algorithm Theory - SWAT 2008, 11th Scandinavian Workshop on Algorithm Theory, Gothenburg, Sweden, July 2-4, 2008, Proceedings; 01/2008
