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International Workshop on Algorithms and Computation

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Combinatorial Optimization with Noisy Inputs: How Can We Separate the Wheat from the Chaff?

Combinatorial Optimization with Noisy Inputs: How Can We Separate the Wheat from the Chaff?

  • Peter Widmayer18 
  • Conference paper
  • 679 Accesses

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7157)

Abstract

We postulate that real world data are almost always noisy, and an exact solution to a noisy input instance of a combinatorial optimization problem is not what we really want. Noise, or input data uncertainty, has a variety of reasons, such as for instance the need to estimate data based on imprecise measurements or on predictions (drawn from historical data and expected modifications). There is a variety of popular ways to deal with this uncertainty problem. In lucky cases in which the input data distribution is known, one might aim at obtaining a solution that is good in expectation. A different, promising way to handle uncertainty is based on the availability of a discrete set of possible problem instances (sometimes reflecting a distribution), so-called scenarios. A solution must be proposed for a set of scenarios as input, and thereafter a single scenario reveals itself as the actual one. The goal here is to achieve a high quality of the proposed solution with respect to the revealed scenario. Stochastic programming can be used to aim at a good solution in expectation that is feasible for most scenarios. In contrast, robust optimization most often aims at a solution that is feasible in all scenarios and has smallest worst case cost. In any case, uncertainty is considered a curse, a burden, a difficult problem that needs to be dealt with at extra computational cost.

Keywords

  • Problem Instance
  • Minimum Span Tree
  • Stochastic Programming
  • Combinatorial Optimization Problem
  • Robust Optimization

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zürich, Switzerland

    Peter Widmayer

Authors
  1. Peter Widmayer
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Editor information

Editors and Affiliations

  1. Graph Drawing and Information Visualization Laboratory, Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Bangladesh

    Md. Saidur Rahman

  2. , Faculty of Engineering, Department of Computer Science, Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

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© 2012 Springer-Verlag Berlin Heidelberg

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Cite this paper

Widmayer, P. (2012). Combinatorial Optimization with Noisy Inputs: How Can We Separate the Wheat from the Chaff?. In: Rahman, M.S., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2012. Lecture Notes in Computer Science, vol 7157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28076-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-28076-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28075-7

  • Online ISBN: 978-3-642-28076-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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