Abstract
We define and study two versions of the bipartite matching problem in the framework of two-stage stochastic optimization with recourse. In one version the uncertainty is in the second stage costs of the edges, in the other version the uncertainty is in the set of vertices that needs to be matched. We prove lower bounds, and analyze efficient strategies for both cases. These problems model real-life stochastic integral planning problems such as commodity trading, reservation systems and scheduling under uncertainty.
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References
Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer, Heidelberg (1997)
Charikar, M., Chekuri, C., Pal, M.: Sampling bounds fpr stochastic optimization. In: APPROX-RANDOM, pp. 257–269 (2005)
Chlebík, M., Chlebíková, J.: Inapproximability results for bounded variants of optimization problems. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol. 2751, pp. 27–38. Springer, Heidelberg (2003)
Dhamdhere, K., Goyal, V., Ravi, R., Singh, M.: How to pay, come what may: Approximation algorithms for demand-robust covering problems. In: FOCS, pp. 367–378 (2005)
Dhamdhere, K., Ravi, R., Singh, M.: On two-stage stochastic minimum spanning trees. In: Jünger, M., Kaibel, V. (eds.) Integer Programming and Combinatorial Optimization. LNCS, vol. 3509, pp. 321–334. Springer, Heidelberg (2005)
Dye, S., Stougie, L., Tomasgard, A.: The stochastic single resource service-provision problem. Naval Research Logistics 50, 257–269 (2003)
Elbassioni, K.M., Katriel, I., Kutz, M., Mahajan, M.: Simultaneous matchings. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 106–115. Springer, Heidelberg (2005)
Flaxman, A.D., Frieze, A.M., Krivelevich, M.: On the random 2-stage minimum spanning tree. In: SODA, pp. 919–926 (2005)
Gupta, A., Pál, M.: Stochastic steiner trees without a root. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1051–1063. Springer, Heidelberg (2005)
Gupta, A., Pál, M., Ravi, R., Sinha, A.: Boosted sampling: approximation algorithms for stochastic optimization. In: STOC, pp. 417–426. ACM, New York (2004)
Gupta, A., Ravi, R., Sinha, A.: An edge in time saves nine: LP rounding approx. algorithms for stochastic network design. In: FOCS, pp. 218–227 (2004)
Immorlica, N., Karger, D., Minkoff, M., Mirrokni, V.S.: On the costs and benefits of procratination: approximation algorithms for stochastic combinatorial optimization problems. In: SODA, pp. 691–700 (2004)
Katriel, I., Kenyon-Mathieu, C., Upfal, E.: Commitment under uncertainty: Two-stage stochastic matching problems. In: ECCC (2007), http://eccc.hpi-web.de/eccc/
Kenyon, C., Rémila, E.: A near-optimal solution to a two-dimensional cutting stock problem. Math. Oper. Res. 25(4), 645–656 (2000)
Kong, N., Schaefer, A.J.: A factor 1/2 approximation algorithm for two-stage stochastic matching problems. Eur. J. of Operational Research 172, 740–746 (2006)
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. of Computing and System Sciences 43, 425–440 (1991)
Ravi, R., Sinha, A.: Hedging uncertainty: Approximation algorithms for stochastic optimization problems. In: Bienstock, D., Nemhauser, G.L. (eds.) Integer Programming and Combinatorial Optimization. LNCS, vol. 3064, pp. 101–115. Springer, Heidelberg (2004)
Raz, R., Safra, S.: A sub-constant error-prob. low-degree test, and a sub-constant error-prob. PCP characterization of NP. In: STOC, pp. 475–484 (1997)
Shmoys, D.B., Sozio, M.: Approximation algorithms for 2-stage stochastic scheduling problems. In: IPCO (2007)
Shmoys, D.B., Swamy, C.: The sample average approximation method for 2-stage stochastic optimization (2004)
Shmoys, D.B., Swamy, C.: Stochastic optimization is almost as easy as deterministic optimization. In: FOCS, pp. 228–237 (2004)
Swamy, C., Shmoys, D.B.: The sampling-based approximation algorithms for multi-stage stochastic optimization. In: FOCS, pp. 357–366 (2005)
Swamy, C., Shmoys, D.B.: Algorithms column: Approximation algorithms for 2-stage stochastic optimization problems. ACM SIGACT News 37(1), 33–46 (2006)
Verweij, B., Ahmed, S., Kleywegt, A.J., Nemhauser, G., Shapiro, A.: The sample average approximation method applied to stochastic routing problems: a computational study. Comp. Optimization and Applications 24, 289–333 (2003)
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Katriel, I., Kenyon-Mathieu, C., Upfal, E. (2007). Commitment Under Uncertainty: Two-Stage Stochastic Matching Problems. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_17
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DOI: https://doi.org/10.1007/978-3-540-73420-8_17
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