An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs
Joint Authors
Pal, Anita
Rana, Akul
Pal, Madhumangal
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-17
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Let G=(V,E) be a simple connected undirected graph.
Each vertex v∈V has a cost c(v) and provides a positive coverage radius R(v).
A distance duv is associated with each edge {u,v}∈E, and d(u,v) is the shortest distance between every pair of vertices u,v∈V.
A vertex v can cover all vertices that lie within the distance R(v), except the vertex itself.
The conditional covering problem is to minimize the sum of the costs required to cover all the vertices in G.
This problem is NP-complete for general graphs, even it remains NP-complete for chordal graphs.
In this paper, an O(n2) time algorithm to solve a special case of the problem in a trapezoid graph is proposed, where n is the number of vertices of the graph.
In this special case, duv=1 for every edge {u,v}∈E, c(v)=c for every v∈V(G), and R(v)=R, an integer >1, for every v∈V(G).
A new data structure on trapezoid graphs is used to solve the problem.
American Psychological Association (APA)
Rana, Akul& Pal, Anita& Pal, Madhumangal. 2011. An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs. ISRN Discrete Mathematics،Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-454980
Modern Language Association (MLA)
Rana, Akul…[et al.]. An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs. ISRN Discrete Mathematics No. 2011 (2011), pp.1-10.
https://search.emarefa.net/detail/BIM-454980
American Medical Association (AMA)
Rana, Akul& Pal, Anita& Pal, Madhumangal. An Efficient Algorithm to Solve the Conditional Covering Problem on Trapezoid Graphs. ISRN Discrete Mathematics. 2011. Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-454980
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454980