Abstract
The “Constraint Bipartite Vertex Cover” problem (CBVC for short) is: given a bipartite graph G with n vertices and two positive integers k 1, k 2, is there a vertex cover taking at most k1 vertices from one and at most k 2 vertices from the other vertex set of G? CBVC is NP-complete. It formalizes the spare allocation problem for reconfigurable arrays, an important problem from VLSI manufacturing.
We provide the first nontrivial so-called “fixed parameter” algorithm for CBVC, running in time \( O(1.3999^{k_1 + k_2 } + (k_1 + k_2 )n) \). Our algorithm is efficient for small values of k 1 and k 2, as occurring in applications.
Partially supported by a Feodor Lynen fellowship of the Alexander von Humboldt-Stiftung, Bonn, and the Center for Discrete Mathematics, Theoretical Computer Science and Applications (DIMATIA), Prague.
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Fernau, H., Niedermeier, R. (1999). An Efficient Exact Algorithm for Constraint Bipartite Vertex Cover. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_35
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DOI: https://doi.org/10.1007/3-540-48340-3_35
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