HEAL DSpace

Colored Simultaneous Geometric Embeddings and Universal Pointsets

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dc.contributor.author Brandes, U en
dc.contributor.author Erten, C en
dc.contributor.author Estrella-Balderrama, A en
dc.contributor.author Fowler, JJ en
dc.contributor.author Frati, F en
dc.contributor.author Geyer, M en
dc.contributor.author Gutwenger, C en
dc.contributor.author Hong, SH en
dc.contributor.author Kaufmann, M en
dc.contributor.author Kobourov, SG en
dc.contributor.author Liotta, G en
dc.contributor.author Mutzel, P en
dc.contributor.author Symvonis, A en
dc.date.accessioned 2014-03-01T02:04:28Z
dc.date.available 2014-03-01T02:04:28Z
dc.date.issued 2011 en
dc.identifier.issn 0178-4617 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/29433
dc.subject Simultaneous embedding en
dc.subject Simultaneous geometric embedding en
dc.subject Colored simultaneous embedding en
dc.subject Universal pointsets en
dc.subject Graph drawing en
dc.subject.classification Computer Science, Software Engineering en
dc.subject.classification Mathematics, Applied en
dc.subject.other PLANAR GRAPHS en
dc.subject.other FIXED EDGES en
dc.subject.other DRAWINGS en
dc.subject.other TREES en
dc.title Colored Simultaneous Geometric Embeddings and Universal Pointsets en
heal.type journalArticle en
heal.language English en
heal.publicationDate 2011 en
heal.abstract Universal pointsets can be used for visualizing multiple relationships on the same set of objects or for visualizing dynamic graph processes. In simultaneous geometric embeddings, the same point in the plane is used to represent the same object as a way to preserve the viewer's mental map. In colored simultaneous embeddings this restriction is relaxed, by allowing a given object to map to a subset of points in the plane. Specifically, consider a set of graphs on the same set of n vertices partitioned into k colors. Finding a corresponding set of k-colored points in the plane such that each vertex is mapped to a point of the same color so as to allow a straight-line plane drawing of each graph is the problem of colored simultaneous geometric embedding. For n-vertex paths, we show that there exist universal pointsets of size n, colored with two or three colors. We use this result to construct colored simultaneous geometric embeddings for a 2-colored tree together with any number of 2-colored paths, and more generally, a 2-colored outerplanar graph together with any number of 2-colored paths. For n-vertex trees, we construct small near-universal pointsets for 3-colored caterpillars of size n, 3-colored radius-2 stars of size n+3, and 2-colored spiders of size n. For n-vertex outerplanar graphs, we show that these same universal pointsets also suffice for 3-colored K (3)-caterpillars, 3-colored K (3)-stars, and 2-colored fans, respectively. We also present several negative results, showing that there exist a 2-colored planar graph and pseudo-forest, three 3-colored outerplanar graphs, four 4-colored pseudo-forests, three 5-colored pseudo-forests, five 5-colored paths, two 6-colored biconnected outerplanar graphs, three 6-colored cycles, four 6-colored paths, and three 9-colored paths that cannot be simultaneously embedded. en
heal.publisher SPRINGER en
heal.journalName ALGORITHMICA en
dc.identifier.isi ISI:000289242100005 en
dc.identifier.volume 60 en
dc.identifier.issue 3 en
dc.identifier.spage 569 en
dc.identifier.epage 592 en


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