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Author, Editor
Author(s):
Andreou, Maria
Fotakis, Dimitris
Nikoletseas, Sotiris
Papadopoulou, Vicky
Spirakis, Paul G.
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Not MPG Author(s):
Andreou, Maria
Nikoletseas, Sotiris
Papadopoulou, Vicky
Spirakis, Paul G.
Editor(s):
Diks, Krzysztof
Rytter, Wojciech
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Not MPII Editor(s):
Diks, Krzysztof
Rytter, Wojciech
BibTeX cite key*:
AFNPS02
Title, Booktitle
Title*:
On Radiocoloring Hierarchically Specified Planar Graphs: PSPACE-Completeness and Approximations
Attachment(s)
:
mfcs02.ps (314.91 KB)
Booktitle*:
Mathematical Foundations of Computer Science 2002 : 27th International Symposium, MFCS 2002
Event, URLs
URL of the conference:
http://mfcs.mimuw.edu.pl:9080/
URL for downloading the paper:
Event Address*:
Warsaw, Poland
Language:
English
Event Date*
(no longer used):
-- August 26-30, 2002
Organization:
Event Start Date:
26 August 2002
Event End Date:
30 August 2002
Publisher
Name*:
Springer
URL:
http://www.springer.de
Address*:
Berlin, Germany
Type:
Vol, No, Year, pp.
Series:
Lecture Notes in Computer Science
Volume:
2420
Number:
Month:
August
Pages:
81-92
Year*:
2002
VG Wort Pages:
ISBN/ISSN:
3-540-44040-2
Sequence Number:
DOI:
Note, Abstract, ©
(LaTeX) Abstract:
Hierarchical specifications of graphs have been widely used in many important applications, such as VLSI design, parallel programming and software engineering. A well known hierarchical specification model, considered in this work, is that of Lengauer [9, 10] referred to as L-specifications. In this paper we discuss a restriction on the L-specifications resulting to graphs which we call Well-Separated (WS). This class is characterized by a polynomial time (to the size of the specification of the graph) testable combinatorial property.
In this work we study the Radiocoloring Problem (RCP) on WS L-specified hierarchical planar graphs. The optimization version of RCP studied here, consists in assigning colors to the vertices of a graph, such that any two vertices of distance at most two get different colors. The objective here is to minimize the number of colors used. This problem is equivalent to the problem of vertex coloring the square of a graph $G$, $G^2$, where $G^2$ has the same vertex set as $G$ and there is an edge between any two vertices of $G^2$ if their distance in $G$ is at most 2.
We first show that RCP is PSPACE-complete for WS L-specified hierarchical planar graphs. Second, we present a polynomial time 3-approximation algorithm as well as a more efficient 4-approximation algorithm for RCP on graphs of this class.
We note that, the best currently known approximation ratio for the RCP on ordinary (non-hierarchical) planar graphs of general degree is 2 ([6, 1]). Note also that the only known results on any kind of coloring problems have been shown for another special kind of hierarchical graphs (unit disk graphs) achieving a 6-approximation solution [13].
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Access Level:
Public
Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
Audience:
Expert
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort
BibTeX Entry:
@INPROCEEDINGS
{
AFNPS02
,
AUTHOR = {Andreou, Maria and Fotakis, Dimitris and Nikoletseas, Sotiris and Papadopoulou, Vicky and Spirakis, Paul G.},
EDITOR = {Diks, Krzysztof and Rytter, Wojciech},
TITLE = {On Radiocoloring Hierarchically Specified Planar Graphs: PSPACE-Completeness and Approximations},
BOOKTITLE = {Mathematical Foundations of Computer Science 2002 : 27th International Symposium, MFCS 2002},
PUBLISHER = {Springer},
YEAR = {2002},
VOLUME = {2420},
PAGES = {81--92},
SERIES = {Lecture Notes in Computer Science},
ADDRESS = {Warsaw, Poland},
MONTH = {August},
ISBN = {3-540-44040-2},
}
Entry last modified by Uwe Brahm, 03/02/2010
Edit History (please click the blue arrow to see the details)
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Editor(s)
Dimitris Fotakis
Created
11/21/2002 04:31:14 PM
Revisions
12.
11.
10.
9.
8.
Editor(s)
Uwe Brahm
Christine Kiesel
Christine Kiesel
Christine Kiesel
Christine Kiesel
Edit Dates
01/20/2009 07:09:41 PM
28.08.2003 15:56:15
28.08.2003 15:38:40
26.08.2003 15:05:03
20.06.2003 15:43:39
Attachment Section
Attachment Section
View attachments here:
mfcs02.ps
mfcs02.ps