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Workshop on Algorithms and Data Structures

WADS 1995: Algorithms and Data Structures pp 109–121Cite as

Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 955))

Abstract

We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to motion planning, Voronoi diagrams, visibility, and geometric optimization.

by NSF Grants CCR-91-22103 and CCR-93-11127, by a Max-Planck Research Award, and by grants from the U.S.-Israeli Binational Science Foundation, the Israel Science Fund administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Micha Sharir

  2. Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA

    Micha Sharir

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  1. Micha Sharir
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Editor information

Selim G. Akl Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1995 Springer-Verlag Berlin Heidelberg

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Sharir, M. (1995). Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_55

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  • DOI: https://doi.org/10.1007/3-540-60220-8_55

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  • Online ISBN: 978-3-540-44747-4

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