Abstract
The concept of reoptimization models the following question: Given an instance of an optimization problem together with an optimal solution, does this knowledge help for finding a high-quality solution for a locally modified instance?
We briefly survey the known results about reoptimization and consider a generalization of the model where not only one optimal solution is given, but the set of all optimal solutions for an instance is available for free. We use the traveling salesman problem as an example to prove that there exist problems for which this additional knowledge does not help at all for improving the approximability.
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References
Hromkovič, J.: Algorithmics for Hard Problems. Introduction to Combinatorial Optimization, Randomization, Approximation, and Heuristics. In: Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2003)
Sahni, S., Gonzalez, T.F.: P-complete approximation problems. Journal of the ACM 23(3), 555–565 (1976)
Schäffter, M.W.: Scheduling with forbidden sets. Discrete Applied Mathematics 72(1-2), 155–166 (1997)
van Hoesel, S., Wagelmans, A.: On the complexity of postoptimality analysis of 0/1 programs. Discrete Applied Mathematics 91(1-3), 251–263 (1999)
Archetti, C., Bertazzi, L., Speranza, M.G.: Reoptimizing the traveling salesman problem. Networks 42(3), 154–159 (2003)
Ausiello, G., Escoffier, B., Monnot, J., Paschos, V.T.: Reoptimization of minimum and maximum traveling salesman’s tours. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 196–207. Springer, Heidelberg (2006)
Böckenhauer, H.-J., Forlizzi, L., Hromkovič, J., Kneis, J., Kupke, J., Proietti, G., Widmayer, P.: Reusing optimal TSP solutions for locally modified input instances (extended abstract). In: Navarro, G., Bertossi, L.E., Kohayakawa, Y. (eds.) Proc. of the 4th IFIP International Conference on Theoretical Computer Science (TCS 2006). IFIP, vol. 209, pp. 251–270. Springer, New York (2006)
Böckenhauer, H.-J., Komm, D.: Reoptimization of the metric deadline TSP. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 156–167. Springer, Heidelberg (2008)
Bilò, D., Böckenhauer, H.-J., Hromkovič, J., Královič, R., Mömke, T., Widmayer, P., Zych, A.: Reoptimization of steiner trees. In: Gudmundsson, J. (ed.) SWAT 2008. LNCS, vol. 5124, pp. 258–269. Springer, Heidelberg (2008)
Böckenhauer, H.-J., Hromkovič, J., Královič, R., Mömke, T., Rossmanith, P.: Reoptimization of Steiner trees: Changing the terminal set. Theoretical Computer Science 410(36), 3428–3435 (2009)
Escoffier, B., Milanič, M., Paschos, V.T.: Simple and fast reoptimizations for the Steiner tree problem. Algorithmic Operations Research 4(2), 86–94 (2009)
Böckenhauer, H.-J., Freiermuth, K., Hromkovič, J., Mömke, T., Sprock, A., Steffen, B.: The Steiner tree problem with sharpened triangle inequality: hardness and reoptimization. In: Calamoneri, T., Diaz, J. (eds.) CIAC 2010. LNCS, vol. 6078, pp. 180–191. Springer, Heidelberg (2010)
Bilò, D., Böckenhauer, H.-J., Komm, D., Královič, R., Mömke, T., Seibert, S., Zych, A.: Reoptimization of the shortest common superstring problem. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 78–91. Springer, Heidelberg (2009)
Bilò, D., Böckenhauer, H.-J., Komm, D., Královič, R., Mömke, T., Seibert, S., Zych, A.: Reoptimization of the shortest common superstring problem. Algorithmica (2010) (to appear)
Archetti, C., Bertazzi, L., Speranza, M.G.: Reoptimizing the 0-1 knapsack problem. Technical Report 267, University of Brescia (2006)
Bilò, D., Widmayer, P., Zych, A.: Reoptimization of weighted graph and covering problems. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 201–213. Springer, Heidelberg (2009)
Böckenhauer, H.-J., Hromkovič, J., Mömke, T., Widmayer, P.: On the hardness of reoptimization. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 50–65. Springer, Heidelberg (2008)
Papadimitriou, C.H., Yannakakis, M.: The traveling salesman problem with distances one and two. Mathematics of Operations Research 18(1), 1–11 (1993)
Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University (1976)
Böckenhauer, H.-J., Forlizzi, L., Hromkovič, J., Kneis, J., Kupke, J., Proietti, G., Widmayer, P.: On the approximability of TSP on local modifications of optimally solved instances. Algorithmic Operations Research 2(2), 83–93 (2007)
Bern, M.W., Plassmann, P.E.: The Steiner problem with edge lengths 1 and 2. Information Processing Letters 32(4), 171–176 (1989)
Dreyfus, S.E., Wagner, R.A.: The Steiner problem in graphs. Networks 1(/72), 195–207 (1971)
Papadimitriou, C.H., Steiglitz, K.: Some examples of difficult traveling salesman problems. Operations Research 26, 434–443 (1978)
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Böckenhauer, HJ., Hromkovič, J., Sprock, A. (2011). Knowing All Optimal Solutions Does Not Help for TSP Reoptimization. In: Kelemen, J., Kelemenová, A. (eds) Computation, Cooperation, and Life. Lecture Notes in Computer Science, vol 6610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20000-7_2
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DOI: https://doi.org/10.1007/978-3-642-20000-7_2
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