The np-hard independent set problem is to determine for a given graph g and an integer k whether g contains a set of k pairwise non-adjacent vertices. The problem has numerous applications in scheduling, including resource allocation and steel manufacturing. There, one encounters restricted graph classes such as 2-union graphs, which are edge-wise unions of two interval graphs on the same vertex set, or strip graphs, where additionally one of the two interval graphs is a disjoint union of cliques.we prove np-hardness of independent set on a very restricted subclass of 2-union graphs and identify natural parameterizations to chart the possibilities and limitations of effective polynomial-time preprocessing (kernelization) and fixed-parameter algorithms. Our algorithms benefit from novel formulations of the computational problems in terms of (list-)colored interval graphs.
|Title of host publication||Algorithms and Computation|
|Subtitle of host publication||23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 2012 Proceedings|
|Editors||Kun-Mao Chao, Tsan-sheng Hsu, Der-Tsai Lee|
|Publication status||Published - 2012|
|Series||Lecture Notes in Computer Science|
van Bevern, R., Mnich, M., Niedermeier, R., & Weller, M. (2012). Interval Scheduling and Colorful Independent Sets. In K-M. Chao, T. Hsu, & D-T. Lee (Eds.), Algorithms and Computation: 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, December 2012 Proceedings (Vol. 7676, pp. 247-256). Springer. Lecture Notes in Computer Science, Vol.. 7676 https://doi.org/10.1007/978-3-642-35261-4_28