Smoothed Analysis of Integer Programming

  • Heiko Röglin
  • Berthold Vöcking
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3509)


We present a probabilistic analysis of integer linear programs (ILPs). More specifically, we study ILPs in a so-called smoothed analysis in which it is assumed that first an adversary specifies the coefficients of an integer program and then (some of) these coefficients are randomly perturbed, e.g., using a Gaussian or a uniform distribution with small standard deviation. In this probabilistic model, we investigate structural properties of ILPs and apply them to the analysis of algorithms. For example, we prove a lower bound on the slack of the optimal solution. As a result of our analysis, we are able to specify the smoothed complexity of classes of ILPs in terms of their worst case complexity. For example, we obtain polynomial smoothed complexity for packing and covering problems with any fixed number of constraints. Previous results of this kind were restricted to the case of binary programs.


Integer Program Probabilistic Analysis Integer Linear Program Knapsack Problem Perturbation Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Heiko Röglin
    • 1
  • Berthold Vöcking
    • 1
  1. 1.Department of Computer ScienceRWTH Aachen 

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