Networks with unicyclic connected components and without short cycles

Walid Ben-Ameur; Makhlouf Hadji; Adam Ouorou

doi:10.1016/j.endm.2010.05.122

Networks with unicyclic connected components and without short cycles

Walid Ben-Ameur, Makhlouf Hadji, Adam Ouorou

Research output: Contribution to journal › Article › peer-review

Abstract

This paper focuses on the design of networks with unicyclic connected components. The size of each cycle should not be less than a given number. A polyhedral study is proposed. Many facets and valid inequalities are derived. Some of them can be exactly separated in polynomial time. Then the network design problem is solved by a cutting plane algorithm based on these inequalities and using a compact formulation issued from the transversality of the bicircular matroid.

Original language	English
Pages (from-to)	961-968
Number of pages	8
Journal	Electronic Notes in Discrete Mathematics
Volume	36
Issue number	C
DOIs	https://doi.org/10.1016/j.endm.2010.05.122
Publication status	Published - 1 Aug 2010

Keywords

Bicircular matroid
Cycles
Networks
Polyhedra

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10.1016/j.endm.2010.05.122

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title = "Networks with unicyclic connected components and without short cycles",

abstract = "This paper focuses on the design of networks with unicyclic connected components. The size of each cycle should not be less than a given number. A polyhedral study is proposed. Many facets and valid inequalities are derived. Some of them can be exactly separated in polynomial time. Then the network design problem is solved by a cutting plane algorithm based on these inequalities and using a compact formulation issued from the transversality of the bicircular matroid.",

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AU - Ouorou, Adam

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AB - This paper focuses on the design of networks with unicyclic connected components. The size of each cycle should not be less than a given number. A polyhedral study is proposed. Many facets and valid inequalities are derived. Some of them can be exactly separated in polynomial time. Then the network design problem is solved by a cutting plane algorithm based on these inequalities and using a compact formulation issued from the transversality of the bicircular matroid.

KW - Bicircular matroid

KW - Cycles

KW - Networks

KW - Polyhedra

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JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

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Networks with unicyclic connected components and without short cycles

Abstract

Keywords

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