Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Accéder directement au contenu
Article Dans Une Revue Algorithmica Année : 2012

Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming

Résumé

The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if the given graph is bipartite with partition U⊎V, and each vertex in U is assigned the list {1}; this subproblem appears in the context of constraint programming as the consistency problem for the extended global cardinality constraint. We show that this subproblem is fixed-parameter tractable when parameterized by the size of the second partite set V. More generally, we show that the general factor problem for bipartite graphs, parameterized by |V|, is fixed-parameter tractable as long as all vertices in U are assigned lists of length 1, but becomes \normalfont W[1] -hard if vertices in U are assigned lists of length at most 2. We establish fixed-parameter tractability by reducing the problem instance to a bounded number of acyclic instances, each of which can be solved in polynomial time by dynamic programming.

Dates et versions

lirmm-00807998 , version 1 (04-04-2013)

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Citer

Gregory Gutin, Eunjung Kim, Arezou Soleimanfallah, Stefan Szeider, Anders Yeo. Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming. Algorithmica, 2012, 64, pp.112-125. ⟨10.1007/s00453-011-9548-8⟩. ⟨lirmm-00807998⟩
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