Edge-swapping algorithms for the minimum fundamental cycle basis problem

Amaldi, E.; Liberti, Leo; Maffioli, Francesco; Maculan, Nelson

doi:10.1007/s00186-008-0255-4

Cited by 12 publications

(12 citation statements)

References 31 publications

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“…Brimberg et al (2009) use a VNS to solve the heaviest k-subgraph problem. Amaldi et al (2009) propose a VNS to tackle the minimum fundamental cycle basis problem.…”

Section: Graph Problemsmentioning

confidence: 99%

Variable neighbourhood search: methods and applications

2009

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Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.

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“…Brimberg et al (2009) use a VNS to solve the heaviest k-subgraph problem. Amaldi et al (2009) propose a VNS to tackle the minimum fundamental cycle basis problem.…”

Section: Graph Problemsmentioning

confidence: 99%

Variable neighbourhood search: methods and applications

2009

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“…Several approximability results have been established for MinFCB [Gal01] and [GA03]. Integer programming formulation and metaheuristics are presented in [ALMM04]. Exact solutions can only be found for small instances of the cycle base problem.…”

Section: Introductionmentioning

confidence: 99%

Minimum cut bases in undirected networks

Bunke¹,

Hamacher²,

Maffioli³

et al. 2010

Discrete Applied Mathematics

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Given an undirected, connected network G = (V, E) with weights on the edges, the cut basis problem is asking for a maximal number of linear independent cuts such that the sum of the cut weights is minimized. Surprisingly, this problem has not attained as much attention as its graph theoretic counterpart, the cycle basis problem. We consider two versions of the problem, the unconstrained and the fundamental cut basis problem. For the unconstrained case, where the cuts in the basis can be of an arbitrary kind, the problem can be written as a multiterminal network flow problem and is thus solvable in strongly polynomial time. The complexity of this algorithm improves the complexity of the best algorithms for the cycle basis problem, such that it is preferable for cycle basis problems in planar graphs. In contrast, the fundamental cut basis problem, where all cuts in the basis are obtained by deleting an edge, each, from a spanning tree T is shown to be NP-hard. We present heuristics, integer programming formulations and summarize first experiences with numerical tests.

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“…Another interesting research line was devoted to graph optimization problems, such as minimum cuts and trees, whose solutions must satisfy a cardinality constraint (Fischetti et al, ; Ehrgott et al., ; Fortz et al., ; Bruglieri et al., , ). During the last years, he studied minimum cycle and cut bases problems (Amaldi et al, ; Bunke et al., ), and optimal flow and routing problems with reload costs, which naturally arise in distribution and service networks.…”

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confidence: 99%