Subexponential parameterized algorithms

  • Authors:

  • Frederic Dorn;Fedor V. Fomin;Dimitrios M. Thilikos

  • Affiliations:

  • Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway;Department of Mathematics, National & Capodistrian University of Athens, Athens, Greece

  • Venue:
  • ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

We present a series of techniques for the design of subexponential parameterized algorithms for graph problems. The design of such algorithms usually consists of two main steps: first find a branch- (or tree-) decomposition of the input graph whose width is bounded by a sublinear function of the parameter and, second, use this decomposition to solve the problem in time that is single exponential to this bound. The main tool for the first step is Bidimensionality Theory. Here we present the potential, but also the boundaries, of this theory. For the second step, we describe recent techniques, associating the analysis of sub-exponential algorithms to combinatorial bounds related to Catalan numbers. As a result, we have 2O(√k) ˙ nO(1) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.