Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102303
Title: Improved Approximation Algorithms for Box Contact Representations
Authors: Bekos, M. A.
van Dijk, T. C.
Fink, M.
Kindermann, P.
Kobourov, S.
Pupyrev, S.
Spoerhase, J.
Wolff, A.
Issue Date: 2017
Publisher: Springer New York LLC
Citation: Improved Approximation Algorithms for Box Contact Representations / M. A. Bekos, T. C. van Dijk, M. Fink, et al. — DOI 10.1007/s00453-016-0121-3 // Algorithmica. — 2017. — Vol. 77. — Iss. 3. — P. 902-920.
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. © 2016, Springer Science+Business Media New York.
Keywords: APPROXIMATION ALGORITHMS
BOX CONTACT REPRESENTATIONS
WORD CLOUDS
ALGORITHMS
DATA MINING
GEOMETRY
GRAPH THEORY
GRAPHIC METHODS
OPTIMIZATION
PROFITABILITY
TREES (MATHEMATICS)
BIPARTITE GRAPHS
BOX CONTACT REPRESENTATIONS
GEOMETRIC PROBLEMS
GEOMETRIC REPRESENTATION
MAXIMUM DEGREE
SEMANTICALLY-RELATED WORDS
WEIGHTED GRAPH
WORD CLOUDS
APPROXIMATION ALGORITHMS
URI: http://hdl.handle.net/10995/102303
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84955618911
PURE ID: 1619691
4ce13a5b-1ad9-4c52-916d-89c47b6e24ac
ISSN: 1784617
DOI: 10.1007/s00453-016-0121-3
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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