Iterative Rounding for Multi-Objective Optimization Problems

  • Fabrizio Grandoni
  • R. Ravi
  • Mohit Singh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)


In this paper we show that iterative rounding is a powerful and flexible tool in the design of approximation algorithms for multi-objective optimization problems. We illustrate that by considering the multi-objective versions of three basic optimization problems: spanning tree, matroid basis and matching in bipartite graphs. Here, besides the standard weight function, we are given k length functions with corresponding budgets. The goal is finding a feasible solution of maximum weight and such that, for all i, the ith length of the solution does not exceed the ith budget. For these problems we present polynomial-time approximation schemes that, for any constant ε> 0 and k ≥ 1, compute a solution violating each budget constraint at most by a factor (1 + ε). The weight of the solution is optimal for the first two problems, and (1 − ε)-approximate for the last one.


Span Tree Budget Constraint Network Design Problem Linear Programming Relaxation Span Tree Problem 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Fabrizio Grandoni
    • 1
  • R. Ravi
    • 2
  • Mohit Singh
    • 3
  1. 1.Department of Computer Science, Systems and ProductionUniversity of Rome Tor VergataItaly
  2. 2.Tepper School of Business, Carnegie Mellon University, Pittsburgh, USA, Supported in part by NSF grant CCF-0728841USA
  3. 3.Microsoft Research, New EnglandCambridgeUSA

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