Algorithms for connected p-centdian problem on block graphs

Liying Kang (), Jianjie Zhou () and Erfang Shan ()
Additional contact information
Liying Kang: Shanghai University
Jianjie Zhou: Shanghai University
Erfang Shan: Shanghai University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 1, No 19, 252-263

Abstract: Abstract We consider the facility location problem of locating a set $$X_p$$ X p of p facilities (resources) on a network (or a graph) such that the subnetwork (or subgraph) induced by the selected set $$X_p$$ X p is connected. Two problems on a block graph G are proposed: one problem is to minimizes the sum of its weighted distances from all vertices of G to $$X_p$$ X p , another problem is to minimize the maximum distance from each vertex that is not in $$X_p$$ X p to $$X_p$$ X p and, at the same time, to minimize the sum of its distances from all vertices of G to $$X_p$$ X p . We prove that the first problem is linearly solvable on block graphs with unit edge length. For the second problem, it is shown that the set of Pareto-optimal solutions of the two criteria has cardinality not greater than n, and can be obtained in $$O(n^2)$$ O ( n 2 ) time, where n is the number of vertices of the block graph G.

Keywords: Connected p-center; Median; Centdian; Block graphs (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-016-0058-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-016-0058-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-016-0058-0

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().