Now showing items 1-5 of 5

    • 1.5-Approximation for treewidth of graphs excluding a graph with one crossing as a minor 

      Demaine, Erik D.; Hajiaghayi, Mohammad Taghi; Thilikos Touloupas, Dimitrios (2002-05)
      External research report
      Open Access
      We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for ...
    • Bidimensional parameters and local treewidth 

      Demaine, Erik D.; Fomin, Fedor V.; Hajiaghayi, Mohammad Taghi; Thilikos Touloupas, Dimitrios (2003-10)
      External research report
      Open Access
      For several graph theoretic parameters such as vertex cover and dominating set, it is known that if their values are bounded by k then the treewidth of the graph is bounded by some function of k. This fact is used as the ...
    • Exponential speedup of fixed parameter algorithms on K_{3,3}-minor-free or K_{5}-minor-free graphs 

      Hajiaghayi, Mohammad Taghi; Demaine, Erik D.; Thilikos Touloupas, Dimitrios (2002-03)
      External research report
      Open Access
      We present a fixed parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of the K_{5} or K_3,3 as a minor in time O(3^{6sqrt{34 k}}n^{O(1)}). In fact, we present our ...
    • Fast approximation schemes for K_{3,3}-minor-free or K_{5}-minor-free graphs 

      Hajiaghayi, Mohammad Taghi; Nishimura, Naomi; Ragde, Prabhakar; Thilikos Touloupas, Dimitrios (2002-05)
      External research report
      Open Access
      As the class of graphs of bounded treewidth is of limited size, we need to solve NP-hard problems for wider classes of graphs than this class. Eppstein introduced a new concept which can be considered as a generalization ...
    • Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs 

      Demaine, Erik D.; Fomin, Fedor V.; Hajiaghayi, Mohammad Taghi; Thilikos Touloupas, Dimitrios (2003-09)
      External research report
      Open Access
      The (k,r)-center problem} asks whether an input graph G has atr most k vertices (called centers) such that every vertex of $ is within distance at most r from some center. In this paper we prove that the (k,r)-center ...