Dynamic conflict-free colorings in the plane

M.T. de Berg, A. Markovic

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

1 Citaat (Scopus)

Samenvatting

We study dynamic conflict-free colorings in the plane, where the goal is to maintain a conflict-free coloring (CF-coloring for short) under insertions and deletions. - First we consider CF-colorings of a set S of unit squares with respect to points. Our method maintains a CF-coloring that uses O(log n) colors at any time, where n is the current number of squares in S, at the cost of only O(log n) recolorings per insertion or deletion We generalize the method to rectangles whose sides have lengths in the range [1, c], where c is a fixed constant. Here the number of used colors becomes O(log^2 n). The method also extends to arbitrary rectangles whose coordinates come from a fixed universe of size N, yielding O(log^2 N log^2 n) colors. The number of recolorings for both methods stays in O(log n). - We then present a general framework to maintain a CF-coloring under insertions for sets of objects that admit a unimax coloring with a small number of colors in the static case. As an application we show how to maintain a CF-coloring with O(log^3 n) colors for disks (or other objects with linear union complexity) with respect to points at the cost of O(log n) recolorings per insertion. We extend the framework to the fully-dynamic case when the static unimax coloring admits weak deletions. As an application we show how to maintain a CF-coloring with O(sqrt(n) log^2 n) colors for points with respect to rectangles, at the cost of O(log n) recolorings per insertion and O(1) recolorings per deletion. These are the first results on fully-dynamic CF-colorings in the plane, and the first results for semi-dynamic CF-colorings for non-congruent objects.
Originele taal-2Engels
TitelISAAC 2017 : 28th International Symposium on Algorithms and Computation
RedacteurenTakeshi Tokuyama, Yoshio Okamoto
Plaats van productieDagstuhl
UitgeverijSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Pagina's27:1-27:13
Volume92
ISBN van elektronische versie9783959770545
ISBN van geprinte versie978-3-95977-054-5
DOI's
StatusGepubliceerd - 2017
Evenement28th International Symposium on Algorithms and Computation (ISAAC 2017) - Phuket, Thailand
Duur: 9 dec 201712 dec 2017
Congresnummer: 28
http://aiat.in.th/isaac2017/

Publicatie series

NaamLeibniz International Proceedings in Informatics, LIPIcs
Volume92
ISSN van geprinte versie1868-8969

Congres

Congres28th International Symposium on Algorithms and Computation (ISAAC 2017)
Verkorte titelISAAC 2017
LandThailand
StadPhuket
Periode9/12/1712/12/17
Internet adres

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