Abstract
In the multiway cut problem we are given a weighted undirected graph \(G=(V,E)\) and a set \(T \subseteq V\) of k terminals. The goal is to find a minimum weight set of edges \(E' \subseteq E\) with the property that by removing \(E'\) from G all the terminals become disconnected. In this paper we present a simple local search approximation algorithm for the multiway cut problem with approximation ratio \(2-\frac{2}{k}\). We present an experimental evaluation of the performance of our local search algorithm and show that it greatly outperforms the isolation heuristic of Dalhaus et al. and it has similar performance as the much more complex algorithms of Calinescu et al., Sharma and Vondrak, and Buchbinder et al. which have the currently best known approximation ratios for this problem.
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Notes
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References
Alpert, C.J., Kahng, A.B.: Recent directions in netlist partitioning: a survey. Integr. VLSI J. 19(1–2), 1–81 (1995)
Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for k-median and facility location problems. SIAM J. Comput. 33(3), 544–562 (2004)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23(11), 1222–1239 (2001)
Buchbinder, N., Naor, J.S., Schwartz, R.: Simplex partitioning via exponential clocks and the multiway cut problem. In: ACM STOC, pp. 535–544. ACM (2013)
Buchbinder, N., Schwartz, R., Weizman, B.: Simplex transformations and the multiway cut problem. In: ACM-SIAM SODA, pp. 2400–2410. SIAM (2017)
Călinescu, G., Karloff, H., Rabani, Y.: An improved approximation algorithm for multiway cut. In: ACM STOC, pp. 48–52. ACM (1998)
Cunningham, W.H., Tang, L.: Optimal 3-terminal cuts and linear programming. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, pp. 114–125. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48777-8_9
Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864–894 (1994)
Karger, D.R., Klein, P., Stein, C., Thorup, M., Young, N.E.: Rounding algorithms for a geometric embedding of minimum multiway cut. Math. Oper. Res. 29(3), 436–461 (2004)
Lawler, E.L.: Combinatorial optimization: networks and matroids. Courier Corporation (1976)
Lee, C.H., Kim, M., Park, C.I.: An efficient k-way graph partitioning algorithm for task allocation in parallel computing systems. In: First International Conference on Systems Integration, pp. 748–751. IEEE (1990)
Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Layout. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-322-92106-2
Sharma, A., Vondrák, J.: Multiway cut, pairwise realizable distributions, and descending thresholds. In: STOC, pp. 724–733. ACM (2014)
Stone, H.S.: Multiprocessor scheduling with the aid of network flow algorithms. IEEE Trans. Softw. Eng. 1, 85–93 (1977)
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Bloch-Hansen, A., Samei, N., Solis-Oba, R. (2021). Experimental Evaluation of a Local Search Approximation Algorithm for the Multiway Cut Problem. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_28
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