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Constraint Generation Algorithm for the Minimum Connectivity Inference Problem

  • Édouard Bonnet
  • Diana-Elena Fălămaş
  • Rémi WatrigantEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11544)

Abstract

Given a hypergraph H, the Minimum Connectivity Inference problem asks for a graph on the same vertex set as H with the minimum number of edges such that the subgraph induced by every hyperedge of H is connected. This problem has received a lot of attention these recent years, both from a theoretical and practical perspective, leading to several implemented approximation, greedy and heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear Programming (MILP) formulations have been experimented, all representing connectivity constraints by the means of graph flows. In this work, we investigate the efficiency of a constraint generation algorithm, where we iteratively add cut constraints to a simple ILP until a feasible (and optimal) solution is found. It turns out that our method is faster than the previous best flow-based MILP algorithm on random generated instances, which suggests that a constraint generation approach might be also useful for other optimization problems dealing with connectivity constraints. At last, we present the results of an enumeration algorithm for the problem.

Keywords

Hypergraph Constraint generation algorithm Connectivity problem 

Notes

Acknowledgment

We would like to thank Muhammad Abid Dar, Andreas Fischer, John Martinovic and Guntram Scheithauer for providing us the source code of their algorithm [10].

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Édouard Bonnet
    • 1
  • Diana-Elena Fălămaş
    • 1
    • 2
  • Rémi Watrigant
    • 1
    Email author
  1. 1.Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIPLyon Cedex 07France
  2. 2.Technical University of Cluj-NapocaCluj-NapocaRomania

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