Practical Minimum Path Cover

Authors Manuel Cáceres , Brendan Mumey , Santeri Toivonen, Alexandru I. Tomescu



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Manuel Cáceres
  • Department of Computer Science, University of Helsinki, Finland
  • Department of Computer Science, Aalto University, Finland
Brendan Mumey
  • School of Computer Science, Montana State University, Bozeman, MT, USA
Santeri Toivonen
  • Department of Computer Science, University of Helsinki, Finland
Alexandru I. Tomescu
  • Department of Computer Science, University of Helsinki, Finland

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Manuel Cáceres, Brendan Mumey, Santeri Toivonen, and Alexandru I. Tomescu. Practical Minimum Path Cover. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SEA.2024.3

Abstract

Computing a minimum path cover (MPC) of a directed acyclic graph (DAG) is a fundamental problem with a myriad of applications, including reachability. Although it is known how to solve the problem by a simple reduction to minimum flow, recent theoretical advances exploit this idea to obtain algorithms parameterized by the number of paths of an MPC, known as the width. These results obtain fast [Mäkinen et al., TALG 2019] and even linear time [Cáceres et al., SODA 2022] algorithms in the small-width regime. In this paper, we present the first publicly available high-performance implementation of state-of-the-art MPC algorithms, including the parameterized approaches. Our experiments on random DAGs show that parameterized algorithms are orders-of-magnitude faster on dense graphs. Additionally, we present new fast pre-processing heuristics based on transitive edge sparsification. We show that our heuristics improve MPC-solvers by orders of magnitude.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Network flows
Keywords
  • minimum path cover
  • directed acyclic graph
  • maximum flow
  • parameterized algorithms
  • edge sparsification
  • algorithm engineering

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