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Dynamic construction of abstract Voronoi diagrams

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Abstract

The abstract Voronoi diagram (AVD) introduced by R. Klein is a generalization of various concrete Voronoi diagrams—data structures actively used in the last decades for solving theoretical and practical geometric problems. This paper presents a fully dynamic algorithm for AVD construction based on Klein's incremental approach. It needs O(n) worst-case time for a new site insertion in an AVD with n sites. For the first time a possibility of effective site deletion without full reconstruction of AVD is proved. The proposed method for site deletion requires O(mn) expected time, where m is the number of invisible sites, and O(n) if invisible sites are not allowed. The dynamic algorithm consumes O(n) memory at any moment.

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Authors and Affiliations

  1. Moscow State Institute of Electronic Technology (Technical University), Moscow, Russia

    K. K. Malinauskas

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  1. K. K. Malinauskas
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Correspondence to K. K. Malinauskas.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 133–146, 2007.

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Malinauskas, K.K. Dynamic construction of abstract Voronoi diagrams. J Math Sci 154, 214–222 (2008). https://doi.org/10.1007/s10958-008-9160-x

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  • DOI: https://doi.org/10.1007/s10958-008-9160-x

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