Abstract
With respect to a given plane graph, G, a face cover is defined as a set of faces whose boundaries collectively contain every vertex in G. It is known that, when k is fixed, finding a cover of size k (if indeed any exist) can be accomplished in polynomial time. Recent improvements to face cover algorithms are based on the theory of fixed-parameter tractability and reductions to planar dominating set. A major goal has been to reduce the time required for branching, which is the most computationally-intensive aspect of fixed-parameter tractable methods. The fastest previously-known method for solving planar dominating set requires branching time O(8k n). The main contribution of this paper is a direct and relatively simple O(5k n) face cover branching algorithm. A direct O(n 2) face cover kernelization algorithm is also presented.
This research has been supported in part by the following U.S. funding mechanisms: by the National Science Foundation under grants CCR–0075792 and CCR–0311500, by the Office of Naval Research under grant N00014–01–1–0608, and by the Department of Energy under contract DE–AC05–00OR22725.
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Abu-Khzam, F.N., Langston, M.A. (2004). A Direct Algorithm for the Parameterized Face Cover Problem. In: Downey, R., Fellows, M., Dehne, F. (eds) Parameterized and Exact Computation. IWPEC 2004. Lecture Notes in Computer Science, vol 3162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28639-4_19
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DOI: https://doi.org/10.1007/978-3-540-28639-4_19
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