NDLI: Improved Algorithms for Some Competitive Location Centroid Problems on Paths, Trees and Graphs

Content Provider	Springer Nature Link
Author	Lazar, Avivit Tamir, Arie
Copyright Year	2012
Abstract	We consider a common scenario in competitive location, where two competitors (providers) place their facilities (servers) on a network, and the users, which are modeled by the nodes of the network, can choose between the providers. We assume that each user has an inelastic demand, specified by a positive real weight. A user is fully served by a closest facility. The benefit (gain) of a competitor is his market share, i.e., the total weight (demand) of the users served at his facilities.In our scenario the two providers, called the leader and the follower, sequentially place p and r servers, respectively. After the leader selects the locations for his p servers, the follower will determine the optimal locations for his r servers, that maximize his benefit. An (r,p)-centroid is a set of locations for the p servers of the leader, that will minimize the maximum gain of the follower who can establish r servers.In this paper we focus mainly on the cases where either the leader or the follower can establish only one facility, i.e., either p=1, or r=1. We consider two versions of the model. In the discrete case the facilities can be established only at the nodes, while in the absolute case they can be established anywhere on the network.For the (r,1)-centroid problem, we show that it is strongly NP-hard for a general graph, but can be approximated within a factor e/(e−1). On the other hand, when the graph is a tree, we provide strongly polynomial algorithms for the (r,p)-centroid model, whenever p is fixed. For the (1,1)-centroid problem on a general graph, we improve upon known results, and give the first strongly polynomial algorithm. The discrete (1,p)-centroid problem has been known to be NP-hard even for a subclass of series-parallel graphs with pathwidth bounded by 6. In view of this result, we consider the discrete and absolute (1,p) centroid models on a tree, and present the first strongly polynomial algorithms. Further improvements are shown when the tree is a path.
Starting Page	615
Ending Page	640
Page Count	26
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	66
Issue Number	3
e-ISSN	14320541
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-05-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Competitive location problems Centroids Paths Trees Polynomial algorithms Algorithm Analysis and Problem Complexity Theory of Computation Mathematics of Computing Algorithms Computer Systems Organization and Communication Networks Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Planar Disjoint-Paths Completion

Contracting Graphs to Paths and Trees

The Longest Path Problem Is Polynomial on Cocomparability Graphs

Optimal Algorithms for the Path/Tree-Shaped Facility Location Problems in Trees

All-Pairs Bottleneck Paths in Vertex Weighted Graphs

On Dynamic Shortest Paths Problems

A Preemptive Algorithm for Maximizing Disjoint Paths on Trees

On approximating the longest path in a graph

Computing Optimal Steiner Trees in Polynomial Space

Improved Algorithms for Some Competitive Location Centroid Problems on Paths, Trees and Graphs

Similar Documents

Planar Disjoint-Paths Completion

Contracting Graphs to Paths and Trees

The Longest Path Problem Is Polynomial on Cocomparability Graphs

Optimal Algorithms for the Path/Tree-Shaped Facility Location Problems in Trees

All-Pairs Bottleneck Paths in Vertex Weighted Graphs

On Dynamic Shortest Paths Problems

A Preemptive Algorithm for Maximizing Disjoint Paths on Trees

On approximating the longest path in a graph

Computing Optimal Steiner Trees in Polynomial Space

Improved Algorithms for Some Competitive Location Centroid Problems on Paths, Trees and Graphs