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An Incremental Model for Combinatorial Maximization Problems

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Experimental Algorithms (WEA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4007))

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Abstract

Many combinatorial optimization problems aim to select a subset of elements of maximum value subject to certain constraints. We consider an incremental version of such problems, in which some of the constraints rise over time. A solution is a sequence of feasible solutions, one for each time step, such that later solutions build on earlier solutions incrementally. We introduce a general model for such problems, and define incremental versions of maximum flow, bipartite matching, and knapsack. We find that imposing an incremental structure on a problem can drastically change its complexity. With this in mind, we give general yet simple techniques to adapt algorithms for optimization problems to their respective incremental versions, and discuss tightness of these adaptations with respect to the three aforementioned problems.

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Authors and Affiliations

  1. Cornell University, Ithaca, NY, 14853, USA

    Jeff Hartline & Alexa Sharp

Authors
  1. Jeff Hartline
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  2. Alexa Sharp
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Editor information

Editors and Affiliations

  1. Software Department, Edifici Omega, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Carme Àlvarez

  2. ALBCOM Research Group, Universitat Politècnica de Catalunya, Edifici Ω, Campus Nord, Jordi Girona, 1-3, 08034, Barcelona, Spain

    María Serna

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© 2006 Springer-Verlag Berlin Heidelberg

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Hartline, J., Sharp, A. (2006). An Incremental Model for Combinatorial Maximization Problems. In: Àlvarez, C., Serna, M. (eds) Experimental Algorithms. WEA 2006. Lecture Notes in Computer Science, vol 4007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11764298_4

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  • DOI: https://doi.org/10.1007/11764298_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34597-8

  • Online ISBN: 978-3-540-34598-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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