Abstract
We introduce a general model for time-expanded versions of packing problems with a variety of applications. Our notion for time-expanded packings, which we introduce in two natural variations, requires elements to be part of the solution for several consecutive time steps. Despite the fact that the time-expanded counterparts of most combinatorial optimization problems become computationally hard to solve, we present strong approximation algorithms for general dependence systems and matroids, respectively, depending on the considered variant. More precisely, for both notions of time-expanded packings that we introduce, the approximation guarantees we obtain are at most a small constant-factor worse than the best approximation algorithms for the underlying problem in its non-time-expanded version.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V.V., Marchetti-Spaccamela, M., Protasi, M.: Complexity and Approximation. Springer (1999)
Bar-Noy, A., Bar-Yehuda, R., Freund, A., Naor, J.S., Schieber, B.: A unified approach to approximating resource allocation and scheduling. J. ACM, 735–744 (2000)
Bar-Noy, A., Guha, S.: Approximating the throughput of multiple machines in real-time scheduling. SIAM J. Comput. 31, 331–352 (2002)
Berman, P.: A d/2 approximation for maximum weight independent set in d-claw free graphs. Nordic J. of Computing 7, 178–184 (2000)
Caprara, A.: Packing 2-dimensional bins in harmony. In: Proceedings of the 43rd Symposium on Foundations of Computer Science, FOCS 2002, pp. 490–499 (2002)
Duffin, R.J., Karlovitz, L.A.: An infinite linear program with a duality gap. Management Science 12(1), 122–134 (1965)
Ford, L.R., Fulkerson, D.R.: Constructing maximal dynamic flows from static flows. Operations Research 6(3), 419–433 (1958)
Garey, M.R., Johnson, D.S.: Computers and Intractability. A guide to the theory of NP-completeness. W.H. Freeman and Co. (1979)
Ibarra, O.H., Kim, C.E.: Fast approximation algorithms for the knapsack and sum of subset problems. J. ACM 22, 463–468 (1975)
Jansen, K., Zhang, G.: On rectangle packing: maximizing benefits. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004, pp. 204–213 (2004)
Koch, R., Nasrabadi, E., Skutella, M.: Continuous and discrete flows over time: A general model based on measure theory. Mathematical Methods Of Operations Research 73(3), 301–337 (2011)
Kohli, R., Krishnamurti, R.: A total-value greedy heuristic for the integer knapsack problem. Operations Research Letters 12(2), 65–71 (1992)
Lawler, E.L.: Fast approximation algorithms for knapsack problems. In: Proceedings of the 18th Symposium on Foundations of Computer Science, FOCS 1977, pp. 206–213 (1977)
Lee, C.C., Lee, D.T.: A simple on-line bin-packing algorithm. J. ACM 32, 562–572 (1985)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)
Pinedo, M.L.: Scheduling: Theory, Algorithms and Systems, 3rd edn. Springer (2008)
Schrijver, A.: Combinatorial Optimization, Polyhedra and Efficiency. Springer (2003)
Skutella, M.: An introduction to network flows over time. Research Trends in Combinatorial Optimization, pp. 451–482. Springer (2009)
Sloane, N.J.A.: Sequences A000058 and A007018. The On-Line Encyclopedia of Integer Sequences, http://oeis.org
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adjiashvili, D., Bosio, S., Weismantel, R., Zenklusen, R. (2014). Time-Expanded Packings. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-43948-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43947-0
Online ISBN: 978-3-662-43948-7
eBook Packages: Computer ScienceComputer Science (R0)