Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102766
Title: The bundled crossing number
Authors: Alam, M. J.
Fink, M.
Pupyrev, S.
Issue Date: 2016
Publisher: Springer Verlag
Citation: Alam M. J. The bundled crossing number / M. J. Alam, M. Fink, S. Pupyrev. — DOI 10.1007/978-3-319-50106-2_31 // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). — 2016. — Vol. 9801 LNCS. — P. 399-412.
Abstract: We study the algorithmic aspect of edge bundling. A bundled crossing in a drawing of a graph is a group of crossings between two sets of parallel edges. The bundled crossing number is the minimum number of bundled crossings that group all crossings in a drawing of the graph. We show that the bundled crossing number is closely related to the orientable genus of the graph. If multiple crossings and self-intersections of edges are allowed, the two values are identical; otherwise, the bundled crossing number can be higher than the genus. We then investigate the problem of minimizing the number of bundled crossings. For circular graph layouts with a fixed order of vertices, we present a constant-factor approximation algorithm. When the circular order is not prescribed, we get a 6c/c - 2 -approximation for a graph with n vertices having at least cn edges for c > 2. For general graph layouts, we develop an algorithm with an approximation factor of 6c/c - 3 for graphs with at least cn edges for c > 3. © Springer International Publishing AG 2016.
Keywords: APPROXIMATION ALGORITHMS
DRAWING (GRAPHICS)
VISUALIZATION
ALGORITHMIC ASPECTS
APPROXIMATION FACTOR
CONSTANT-FACTOR APPROXIMATION ALGORITHMS
CROSSING NUMBER
MINIMIZING THE NUMBER OF
MULTIPLE CROSSINGS
ORIENTABLE GENUS
SELF-INTERSECTIONS
GRAPH THEORY
URI: http://hdl.handle.net/10995/102766
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85007303442
PURE ID: 1455378
3469f9cf-cddf-4603-8a50-6d7cf2f88ac7
ISSN: 3029743
ISBN: 9783319501055
DOI: 10.1007/978-3-319-50106-2_31
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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