Improved Approximation Algorithms for Box Contact Representations
AuthorBekos, Michael A.
van Dijk, Thomas C.
AffiliationDepartment of Computer Science, University of Arizona
MetadataShow full item record
CitationImproved Approximation Algorithms for Box Contact Representations 2016, 77 (3):902 Algorithmica
Rights© Springer Science+Business Media New York 2016.
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractWe 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.
Note12 month embargo; First Online: 27 January 2016
VersionFinal accepted manuscript
SponsorsESF EuroGIGA project GraDR; NSF [CCF-1115971, DEB 1053573]