Cutting-plane-based algorithms for two branch vertices related spanning tree problems
A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minim...
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| Published in | Optimization and engineering Vol. 15; no. 4; pp. 855 - 887 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.12.2014
Springer Nature B.V Springer Verlag |
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| Online Access | Get full text |
| ISSN | 1389-4420 1573-2924 |
| DOI | 10.1007/s11081-013-9219-5 |
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| Abstract | A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minimizes the degree sum of branch vertices (MDS). These two problems arise in the design of wavelength-division networks (WDN), when the cost of equipments for enabling multicast communication is to be minimized. After investigating the relations of MBV and MDS with the problem of minimizing the number of leaves in a spanning tree, new formulations based on ILP are proposed for MBV and MDS, along with two cutting plane algorithms for addressing them. A repair function is also introduced for deriving feasible solutions from the candidate trees returned at each iteration of the cutting plane algorithm, as well as a Tabu search procedure for further quality improvement. The resulting hybrid approach is shown to outperform pure ILP formulations and heuristic approaches published earlier. |
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| AbstractList | A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minimizes the degree sum of branch vertices (MDS). These two problems arise in the design of wavelength-division networks (WDN), when the cost of equipments for enabling multicast communication is to be minimized. After investigating the relations of MBV and MDS with the problem of minimizing the number of leaves in a spanning tree, new formulations based on ILP are proposed for MBV and MDS, along with two cutting plane algorithms for addressing them. A repair function is also introduced for deriving feasible solutions from the candidate trees returned at each iteration of the cutting plane algorithm, as well as a Tabu search procedure for further quality improvement. The resulting hybrid approach is shown to outperform pure ILP formulations and heuristic approaches published earlier.[PUBLICATION ABSTRACT] A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minimizes the degree sum of branch vertices (MDS). These two problems arise in the design of wavelength-division networks (WDN), when the cost of equipments for enabling multicast communication is to be minimized. After investigating the relations of MBV and MDS with the problem of minimizing the number of leaves in a spanning tree, new formulations based on ILP are proposed for MBV and MDS, along with two cutting plane algorithms for addressing them. A repair function is also introduced for deriving feasible solutions from the candidate trees returned at each iteration of the cutting plane algorithm, as well as a Tabu search procedure for further quality improvement. The resulting hybrid approach is shown to outperform pure ILP formulations and heuristic approaches published earlier. A branch vertex is a vertex with degree larger than or equal to three. This paper addresses two spanning tree problems in an undirected, simple graph. The first one is to find a spanning tree that minimizes the number of branch vertices (MBV), and the second one is to find a spanning tree that minimizes the degree sum of branch vertices (MDS). These two problems arise in the design of wavelength-division networks (WDN), when the cost of equipments for enabling multicast communication is to be minimized. After investigating the relations of MBV and MDS with the problem of minimizing the number of leaves in a spanning tree, new formulations based on ILP are proposed for MBV and MDS, along with two cutting plane algorithms for addressing them. A repair function is also introduced for deriving feasible solutions from the candidate trees returned at each iteration of the cutting plane algorithm, as well as a Tabu search procedure for further quality improvement. The resulting hybrid approach is shown to outperform pure ILP formulations and heuristic approaches published earlier. |
| Author | Singh, Alok Rossi, André Sundar, Shyam |
| Author_xml | – sequence: 1 givenname: André surname: Rossi fullname: Rossi, André email: andre.rossi@univ-ubs.fr organization: Lab-STICC, CNRS, Université de Bretagne-Sud – sequence: 2 givenname: Alok surname: Singh fullname: Singh, Alok organization: Department of Computer and Information Sciences, University of Hyderabad – sequence: 3 givenname: Shyam surname: Sundar fullname: Sundar, Shyam organization: Department of Computer and Information Sciences, University of Hyderabad |
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| Cites_doi | 10.1016/S0167-5060(08)70356-X 10.1016/j.cor.2004.04.017 10.1112/plms/s3-2.1.69 10.1016/j.ipl.2007.08.030 10.1007/s00186-008-0222-0 10.1023/A:1015391312481 10.1109/35.825645 10.1007/BF02093512 10.1006/jagm.2000.1137 10.1016/S0377-2217(96)00327-X 10.1016/j.osn.2004.11.002 10.1007/s10589-007-9120-2 10.1016/S0140-3664(02)00191-3 10.1049/el:19780233 10.1016/j.dam.2005.05.022 10.1016/j.cor.2005.11.003 10.1016/j.osn.2005.10.001 10.1007/978-1-4615-6089-0 |
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| Keywords | Branch vertex Wavelength-division Matheuristic Tabu search Cutting plane algorithm Spanning tree |
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| Title | Cutting-plane-based algorithms for two branch vertices related spanning tree problems |
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