Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling

Author Takuro Fukunaga

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Takuro Fukunaga
  • Faculty of Science and Engineering, Chuo University, Tokyo, Japan

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Takuro Fukunaga. Integrality Gap of Time-Indexed Linear Programming Relaxation for Coflow Scheduling. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Coflow is a set of related parallel data flows in a network. The goal of the coflow scheduling is to process all the demands of the given coflows while minimizing the weighted completion time. It is known that the coflow scheduling problem admits several polynomial-time 5-approximation algorithms that compute solutions by rounding linear programming (LP) relaxations of the problem. In this paper, we investigate the time-indexed LP relaxation for coflow scheduling. We show that the integrality gap of the time-indexed LP relaxation is at most 4. We also show that yet another polynomial-time 5-approximation algorithm can be obtained by rounding the solutions to the time-indexed LP relaxation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
  • coflow scheduling
  • hypergraph matching
  • approximation algorithm


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