NDLI: Online Coloring and $L(2,1)$-Labeling of Unit Disk Intersection Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Weͅsek, Krzysztof Sokó, Joanna Junosza-Szaniawski, Konstanty Rzaͅżewski, Pawe
Copyright Year	2018
Abstract	In this paper we give a family of online algorithms for the classical coloring and the $L(2,1)$-labeling problems of unit disk intersection graphs. In the $L(2,1)$-labeling we ask for an assignment of nonnegative integers to the vertices of the input graph, such that adjacent vertices get labels that differ by at least 2, and vertices with a common neighbor get different labels. In particular, we present a coloring algorithm with competitive ratio less than 5, which makes it the currently best online coloring algorithm for unit disk intersection graphs. Our algorithms make use of a geometric representation of such graphs and are inspired by previous results but have better competitive ratios. The improvement comes from a novel application of a fractional and a $b$-fold coloring of the plane, which is in turn a variation of the Hadwiger--Nelson problem. Our method can also be adapted successfully for other classes of geometric intersection graphs.
Sponsorship	H2020 European Research Council. Ministerstwo Nauki i Szkolnictwa Wyzszego
Starting Page	1335
Ending Page	1350
Page Count	16
File Format	PDF
ISSN	08954801
DOI	10.1137/16M1097821
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	32
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-06-14
Access Restriction	Subscribed
Subject Keyword	unit disk intersection graphs coloring Graph theory $L(2,1)$-labeling Graph representations online algorithms Coloring of graphs and hypergraphs
Content Type	Text
Resource Type	Article
Subject	Mathematics

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