Integer Programming Formulations for Minimum Spanning Forests and Connected Components in Sparse Graphs

Fan, Neng; Golari, Mehdi

doi:10.1007/978-3-319-12691-3_46

Cited by 11 publications

(2 citation statements)

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“…Over the last couple of decades, as a result of advances in high-performance computing and more efficient algorithms, ILP has achieved considerable success in obtaining optimal solutions to many combinatorial optimization problems. Existing ILP formulations for the MST problem include Martin's Formulation, the Subtour Elimination Formulation, the Cutset Formulation [29][30][31].…”

Section: Related Workmentioning

confidence: 99%

Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency

Wang,

Moran

et al. 2020

Preprint

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This paper provides an optimized cable path planning solution for a tree-topology network in an irregular 2D manifold in a 3D Euclidean space, with an application to the planning of submarine cable networks. Our solution method is based on total cost minimization, where the individual cable costs are assumed to be linear to the length of the corresponding submarine cables subject to latency constraints between pairs of nodes. These latency constraints limit the cable length and number of hops between any pair of nodes. Our method combines the Fast Marching Method (FMM) and a new Integer Linear Programming (ILP) formulation for Minimum Spanning Tree (MST) where there are constraints between pairs of nodes. We note that this problem of MST with constraints is NP-complete. Nevertheless, we demonstrate that ILP running time is adequate for the great majority of existing cable systems. For cable systems for which ILP is not able to find the optimal solution within an acceptable time, we propose an alternative heuristic algorithm based on Prim's algorithm. In addition, we apply our FMM/ILP-based algorithm to a real-world cable path planning example and demonstrate that it can effectively find an MST with latency constraints between pairs of nodes.

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Section: Related Workmentioning

confidence: 99%

Optimal Tree Topology for a Submarine Cable Network With Constrained Internodal Latency

Wang,

Moran

et al. 2020

Preprint

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“…The second constraint comes from the so called subtour elimination constraints, which prevents cycles in any subset N sub ⊂ N . There are actually three of them for forests in general but, according to the discussion of [72], these can be expressed as the single constraint (A.2).…”

Section: Otherwisementioning

confidence: 99%