Fully-dynamic and kinetic conflict-free coloring of intervals with respect to points

M.T. de Berg, T. Leijsen, A. Markovic, A.M. van Renssen, M.J.M. Roeloffzen, G. Woeginger

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

1 Citaat (Scopus)

Samenvatting

We introduce the fully-dynamic conflict-free coloring problem for a set S of intervals in R^1 with respect to points, where the goal is to maintain a conflict-free coloring for S under insertions and deletions. A coloring is conflict-free if for each point p contained in some interval, p is contained in an interval whose color is not shared with any other interval containing p. We investigate trade-offs between the number of colors used and the number of intervals that are recolored upon insertion or deletion of an interval. Our results include: - a lower bound on the number of recolorings as a function of the number of colors, which implies that with O(1) recolorings per update the worst-case number of colors is Omega(log n/log log n), and that any strategy using O(1/epsilon) colors needs Omega(epsilon n^epsilon) recolorings; - a coloring strategy that uses O(log n) colors at the cost of O(log n) recolorings, and another strategy that uses O(1/epsilon) colors at the cost of O(n^epsilon/epsilon) recolorings; - stronger upper and lower bounds for special cases. We also consider the kinetic setting where the intervals move continuously (but there are no insertions or deletions); here we show how to maintain a coloring with only four colors at the cost of three recolorings per event and show this is tight.
Originele taal-2Engels
TitelISAAC 2017 : 28th International Symposium on Algorithms and Computation, 9-12 December 2017, Phuket, Thailand
RedacteurenTakeshi Tokuyama, Yoshio Okamoto
Plaats van productieDagstuhl
UitgeverijSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Pagina's26:1-26:13
ISBN van elektronische versie9783959770545
ISBN van geprinte versie978-3-95977-054-5
DOI's
StatusGepubliceerd - 1 dec 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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  • Citeer dit

    de Berg, M. T., Leijsen, T., Markovic, A., van Renssen, A. M., Roeloffzen, M. J. M., & Woeginger, G. (2017). Fully-dynamic and kinetic conflict-free coloring of intervals with respect to points. In T. Tokuyama, & Y. Okamoto (editors), ISAAC 2017 : 28th International Symposium on Algorithms and Computation, 9-12 December 2017, Phuket, Thailand (blz. 26:1-26:13). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ISAAC.2017.26