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.
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Notes
- 1.
The quotient graph w.r.t. \(X_1\), \(\dots \), \(X_r\) has r vertices \(v_1\), \(\dots \), \(v_r\), and an edge \(v_iv_j\) whenever there is an edge between a vertex of \(X_i\) and a vertex of \(X_j\), \(i \ne j\).
- 2.
A non-trivial partition of a set V is a partition where each set is different from \(\emptyset \) and V.
- 3.
We used the implementation of [10] provided by their authors.
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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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Bonnet, É., Fălămaş, DE., Watrigant, R. (2019). Constraint Generation Algorithm for the Minimum Connectivity Inference Problem. In: Kotsireas, I., Pardalos, P., Parsopoulos, K., Souravlias, D., Tsokas, A. (eds) Analysis of Experimental Algorithms. SEA 2019. Lecture Notes in Computer Science(), vol 11544. Springer, Cham. https://doi.org/10.1007/978-3-030-34029-2_12
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