Dynamic maintenance of planar digraphs, with applications View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1990-06

AUTHORS

Roberto Tamassia, Franco P. Preparata

ABSTRACT

We show that a planarst-graphG admits two total orders on the setV∪E ∪F, whereV, E, andF are respectively the set of vertices, edges, and faces ofG, with ¦V¦ =n. Assuming thatG is to be dynamically modified by means of insertions of edges and expansions of vertices (and their inverses), we exhibit anO(n)-space dynamic data structure for the maintenance of these orders such that an update can be performed in timeO(logn). The discovered structural properties of planarst-graphs provide a unifying theoretical underpinning for several applications, such as dynamic point location in planar monotone subdivisions, dynamic transitive-closure query in planarst-graphs, and dynamic contact-chain query in convex subdivisions. The presented techniques significantly outperform previously known solutions of the same problems. More... »

PAGES

509-527

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01840401

DOI

http://dx.doi.org/10.1007/bf01840401

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1050631860


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