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G. Gutin, Ej Kim, A. Soleimanfallah, St. Szeider, A. Yeo:
"Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming";
Algorithmica, Vol. 64 (2012), No. 1; S. 112 - 125.

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 -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.

http://dx.doi.org/10.1007/s00453-011-9548-8

Projektleitung Stefan Szeider:
The Parameterized Complexity of Reasoning Problems