Modelling and solving central cycle problems with integer programming

We consider the problem of identifying a central subgraph of a given simple connected graph. The case where the subgraph comprises a discrete set of vertices is well known. However, the concept of eccentricity can be extended to connected subgraphs such as: paths, trees and cycles. Methods have been...

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Main Authors: L.R. Foulds, John Wilson, T. Yamaguchi
Format: Default Preprint
Published: 2000
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Online Access:https://hdl.handle.net/2134/2019
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id rr-article-9495062
record_format Figshare
spelling rr-article-94950622000-01-01T00:00:00Z Modelling and solving central cycle problems with integer programming L.R. Foulds (7196288) John Wilson (1256310) T. Yamaguchi (7196345) Other commerce, management, tourism and services not elsewhere classified Cycle centre Cycle centroid Cycle median Graph Heuristic Integer programming Location Business and Management not elsewhere classified We consider the problem of identifying a central subgraph of a given simple connected graph. The case where the subgraph comprises a discrete set of vertices is well known. However, the concept of eccentricity can be extended to connected subgraphs such as: paths, trees and cycles. Methods have been reported which deal with the requirement that the subgraph is a path or a constrained tree. We extend this work to the case where the subgraph is required to be a cycle. We report on computational experience with integer programming models of the problems of identifying cycle centres, cycle medians and cycle centroids, and also on a heuristic based on the first model. The problems have applications in facilities location, particularly the location of emergency facilities, and service facilities. 2000-01-01T00:00:00Z Text Preprint 2134/2019 https://figshare.com/articles/preprint/Modelling_and_solving_central_cycle_problems_with_integer_programming/9495062 CC BY-NC-ND 4.0
institution Loughborough University
collection Figshare
topic Other commerce, management, tourism and services not elsewhere classified
Cycle centre
Cycle centroid
Cycle median
Graph
Heuristic
Integer programming
Location
Business and Management not elsewhere classified
spellingShingle Other commerce, management, tourism and services not elsewhere classified
Cycle centre
Cycle centroid
Cycle median
Graph
Heuristic
Integer programming
Location
Business and Management not elsewhere classified
L.R. Foulds
John Wilson
T. Yamaguchi
Modelling and solving central cycle problems with integer programming
description We consider the problem of identifying a central subgraph of a given simple connected graph. The case where the subgraph comprises a discrete set of vertices is well known. However, the concept of eccentricity can be extended to connected subgraphs such as: paths, trees and cycles. Methods have been reported which deal with the requirement that the subgraph is a path or a constrained tree. We extend this work to the case where the subgraph is required to be a cycle. We report on computational experience with integer programming models of the problems of identifying cycle centres, cycle medians and cycle centroids, and also on a heuristic based on the first model. The problems have applications in facilities location, particularly the location of emergency facilities, and service facilities.
format Default
Preprint
author L.R. Foulds
John Wilson
T. Yamaguchi
author_facet L.R. Foulds
John Wilson
T. Yamaguchi
author_sort L.R. Foulds (7196288)
title Modelling and solving central cycle problems with integer programming
title_short Modelling and solving central cycle problems with integer programming
title_full Modelling and solving central cycle problems with integer programming
title_fullStr Modelling and solving central cycle problems with integer programming
title_full_unstemmed Modelling and solving central cycle problems with integer programming
title_sort modelling and solving central cycle problems with integer programming
publishDate 2000
url https://hdl.handle.net/2134/2019
_version_ 1756514601722183680