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Cost Preserving Dependent Rounding for Allocation Problems

Authors Lars Rohwedder, Arman Rouhani, Leo Wennmann

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  • Theory of computation → Rounding techniques
Keywords
  • Matching
  • Randomized Rounding
  • Santa Claus
  • Approximation Algorithms

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Abstract

We present a dependent randomized rounding scheme, which rounds fractional solutions to integral solutions satisfying certain hard constraints on the output while preserving Chernoff-like concentration properties. In contrast to previous dependent rounding schemes, our algorithm guarantees that the cost of the rounded integral solution does not exceed that of the fractional solution. Our algorithm works for a class of assignment problems with restrictions similar to those of prior works.
In a non-trivial combination of our general result with a classical approach from Shmoys and Tardos [Math. Programm.'93] and more recent linear programming techniques developed for the restricted assignment variant by Bansal, Sviridenko [STOC'06] and Davies, Rothvoss, Zhang [SODA'20], we derive a O(log n)-approximation algorithm for the Budgeted Santa Claus Problem. In this new variant, the goal is to allocate resources with different values to players, maximizing the minimum value a player receives, and satisfying a budget constraint on player-resource allocation costs.

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Lars Rohwedder, Arman Rouhani, and Leo Wennmann. Cost Preserving Dependent Rounding for Allocation Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.127

Author Details

Lars Rohwedder
  • University of Southern Denmark, Odense, Denmark
Arman Rouhani
  • Maastricht University, The Netherlands
Leo Wennmann
  • University of Southern Denmark, Odense, Denmark

Funding

Lars Rohwedder and Leo Wennmann: Supported by Dutch Research Council (NWO) project "The Twilight Zone of Efficiency: Optimality of Quasi-Polynomial Time Algorithms" [grant number OCEN.W.21.268].

References

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