4 research outputs found

    Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

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    International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    An FPT Algorithm for Planar Multicuts with Sources and Sinks on the Outer Face

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    International audienceGiven a list of k source-sink pairs in an edge-weighted graph G, the minimum multicut problem consists in selecting a set of edges of minimum total weight in G, such that removing these edges leaves no path from each source to its corresponding sink. To the best of our knowledge, no non-trivial FPT result for special cases of this problem, which is APX-hard in general graphs for any fixed k ≥ 3, is known with respect to k only. When the graph G is planar, this problem is known to be polynomial-time solvable if k = O(1), but cannot be FPT with respect to k under the Exponential Time Hypothesis. In this paper, we show that, if G is planar and in addition all sources and sinks lie on the outer face, then this problem does admit an FPT algorithm when parameterized by k (although it remains APX-hard when k is part of the input, even in stars). To do this, we provide a new characterization of optimal solutions in this case, and then use it to design a "divide-and-conquer" approach: namely, some edges that are part of any such solution actually define an optimal solution for a polynomial-time solvable multiterminal variant of the problem on some of the sources and sinks (which can be identified thanks to a reduced enumeration phase). Removing these edges from the graph cuts it into several smaller instances, which can then be solved recursively
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