TY - GEN

T1 - Improved approximation algorithms for box contact representations

AU - Bekos, Michael A.

AU - Van Dijk, Thomas C.

AU - Fink, Martin

AU - Kindermann, Philipp

AU - Kobourov, Stephen

AU - Pupyrev, Sergey

AU - Spoerhase, Joachim

AU - Wolff, Alexander

PY - 2014

Y1 - 2014

N2 - 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 show that the problem is APX-complete on bipartite graphs of bounded maximum degree. 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 consider several planar graph classes (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.

AB - 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 show that the problem is APX-complete on bipartite graphs of bounded maximum degree. 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 consider several planar graph classes (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.

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U2 - 10.1007/978-3-662-44777-2_8

DO - 10.1007/978-3-662-44777-2_8

M3 - Conference contribution

AN - SCOPUS:84958522604

SN - 9783662447765

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 87

EP - 99

BT - Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings

PB - Springer-Verlag

T2 - 22nd Annual European Symposium on Algorithms, ESA 2014

Y2 - 8 September 2014 through 10 September 2014

ER -