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
Subjects:	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
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

Modelling and solving central cycle problems with integer programming

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