NDLI: Improved Approximation Algorithms for Box Contact Representations

Content Provider	Springer Nature Link
Author	Bekos, Michael A. Dijk, Thomas C. Fink, Martin Kindermann, Philipp Kobourov, Stephen Pupyrev, Sergey Spoerhase, Joachim Wolff, Alexander
Copyright Year	2016
Abstract	We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called Contact Representation of Word Networks (Crown) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Crown is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, Max-Crown, in which realizing each desired adjacency yields a certain profit. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-complete on bipartite graphs of bounded maximum degree.
Starting Page	902
Ending Page	920
Page Count	19
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	77
Issue Number	3
e-ISSN	14320541
Language	English
Publisher	Springer US
Publisher Date	2016-01-27
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Word clouds Box contact representations Approximation 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

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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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
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