Abstract
The Multicut problem is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NP-completeness and (fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.
Research supported by the Deutsche Forschungsgemeinschaft (DFG), Emmy Noether research group PIAF (fixed-parameter algorithms), NI 369/4.
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References
Booth, K.S., Lueker, G.S.: Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms. Journal of Computer and System Sciences 13, 335–379 (1976)
Costa, M., Létocart, L., Roupin, F.: Minimal Multicut and Maximal Integer Multiflow: a Survey. European Journal of Operational Research 162(1), 55–69 (2005)
Călinescu, G., Fernandes, C.G., Reed, B.: Multicuts in Unweighted Graphs and Digraphs with Bounded Degree and Bounded Tree-Width. Journal of Algorithms 48, 333–359 (2003)
Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The Complexity of Multiterminal Cuts. SIAM Journal on Computing 23(4), 864–894 (1994)
Erdős, P.L., Székely, L.A.: Evolutionary Trees: an Integer Multicommodity Max-Flow–Min-Cut Theorem. Advances in Applied Mathematics 13, 375–389 (1992)
Garg, N., Vazirani, V., Yannakakis, M.: Primal-Dual Approximation Algorithms for Integral Flow and Multicut in Trees. Algorithmica 18(1), 3–20 (1997)
Guo, J., Niedermeier, R.: Exact Algorithms and Applications for Tree-Like Weighted Set Cover. To appear in Journal of Discrete Algorithms (2005)
Guo, J., Niedermeier, R.: Fixed-Parameter Tractability and Data Reduction for Multicut in Trees. Networks 46(3), 124–135 (2005)
Marx, D.: Parameterized Graph Separation Problems. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 71–82. Springer, Heidelberg (2004); Long version to appear in Theoretical Computer Science
Veinott, A.F., Wagner, H.M.: Optimal Capacity Scheduling. Operations Research 10, 518–532 (1962)
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Guo, J., Hüffner, F., Kenar, E., Niedermeier, R., Uhlmann, J. (2006). Complexity and Exact Algorithms for Multicut. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_28
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DOI: https://doi.org/10.1007/11611257_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31198-0
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