• A Simple and fast approach for solving problems on planar graphs 

      Fomin, Fedor V.; Thilikos Touloupas, Dimitrios (2003-12)
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      Accés obert
      It is well known that the celebrated Lipton-Tarjan planar separation theorem, in a combination with a divide-and-conquer strategy leads to many complexity results for planar graph problems. For example, by using this ...
    • Bidimensional parameters and local treewidth 

      Demaine, Erik D.; Fomin, Fedor V.; Hajiaghayi, Mohammad Taghi; Thilikos Touloupas, Dimitrios (2003-10)
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      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 ...
    • Connected graph searching 

      Barrière Figueroa, Eulalia; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos Touloupas, Dimitrios (2010-09-26)
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      In graph searching game the opponents are a set of searchers and a fugitive in a graph. The searchers try to capture the fugitive by applying some sequence moves that include placement, removal, or sliding of a searcher ...
    • Dominating sets and local treewidth 

      Thilikos Touloupas, Dimitrios; Fomin, Fedor V. (2003-09)
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      Accés obert
      It is known that the treewidth of a planar graph with a dominating set of size d is O(sqrt{d}) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. An interesting question ...
    • Dominating sets in planar graphs: branch-width and exponential speed-up 

      Fomin, Fedor V.; Thilikos Touloupas, Dimitrios (2002-12)
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      Accés obert
      Graph minors theory, developed by Robertson & Seymour, provides a list of powerful theoretical results and tools. However, the wide spread opinion in Graph Algorithms community about this theory is that it is mainly of ...
    • 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)
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      Accés obert
      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 ...
    • New upper bounds on the decomposability of planar graphs and fixed parameter algorithms 

      Fomin, Fedor V.; Thilikos Touloupas, Dimitrios (2002-08)
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      Accés obert
      It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a ...
    • On the monotonicity of games generated by symmetric submodular functions 

      Fomin, Fedor V.; Thilikos Touloupas, Dimitrios (2001-02)
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      Submodular functions have appeared to be a key tool for proving the monotonicity of several graph searching games. In this paper we provide a general game theoretic framework able to unify old and new monotonicity ...
    • The price of connectedness in expansions 

      Fomin, Fedor V.; Fraigniaud, Pierre; Thilikos Touloupas, Dimitrios (2004-05)
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      Accés obert
      Expansion is the way of generalizing different graph layout and searching problems. We initiate the study of connected expansion which naturally arises in a number of applications. Our main tool for this investigation ...