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Fixed-Parameter Algorithms for Unsplittable Flow Cover

Authors Andrés Cristi , Mathieu Mari, Andreas Wiese

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Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Fixed parameter tractability
Keywords
  • Unsplittable Flow Cover
  • fixed parameter algorithms
  • approximation algorithms

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Abstract

The Unsplittable Flow Cover problem (UFP-cover) models the well-studied general caching problem and various natural resource allocation settings. We are given a path with a demand on each edge and a set of tasks, each task being defined by a subpath and a size. The goal is to select a subset of the tasks of minimum cardinality such that on each edge e the total size of the selected tasks using e is at least the demand of e. There is a polynomial time 4-approximation for the problem [Bar-Noy et al., STOC 2000] and also a QPTAS [Höhn et al., ICALP 2014]. In this paper we study fixed-parameter algorithms for the problem. We show that it is W[1]-hard but it becomes FPT if we can slightly violate the edge demands (resource augmentation) and also if there are at most k different task sizes. Then we present a parameterized approximation scheme (PAS), i.e., an algorithm with a running time of f(k)⋅ n^O_ε(1) that outputs a solution with at most (1+ε)k tasks or assert that there is no solution with at most k tasks. In this algorithm we use a new trick that intuitively allows us to pretend that we can select tasks from OPT multiple times.

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Andrés Cristi, Mathieu Mari, and Andreas Wiese. Fixed-Parameter Algorithms for Unsplittable Flow Cover. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.42

Author Details

Andrés Cristi
  • Universidad de Chile, Santiago, Chile
Mathieu Mari
  • École Normale Supérieure, Université PSL, Paris, France
Andreas Wiese
  • Universidad de Chile, Santiago, Chile

Funding

  • Cristi, Andrés: Supported by CONICYT-PFCHA/Doctorado Nacional/2018-21180347.
  • Mari, Mathieu: This work was partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).
  • Wiese, Andreas: Partially supported by FONDECYT Regular grant 1170223.

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