TY - JOUR
T1 - Fully Dynamic (Δ+1)-Coloring in O(1) Update Time
AU - Bhattacharya, Sayan
AU - Grandoni, Fabrizio
AU - Kulkarni, Janardhan
AU - Liu, Quanquan C.
AU - Solomon, Shay
N1 - Publisher Copyright:
© 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM.
PY - 2022/4
Y1 - 2022/4
N2 - The problem of (Δ+1)-vertex coloring a graph of maximum degree Δhas been extremely well studied over the years in various settings and models. Surprisingly, for the dynamic setting, almost nothing was known until recently. In SODA'18, Bhattacharya, Chakrabarty, Henzinger and Nanongkai devised a randomized algorithm for maintaining a (Δ+1)-coloring with O(log ") expected amortized update time. In this article, we present an improved randomized algorithm for (Δ+1)-coloring that achieves O(1) amortized update time and show that this bound holds not only in expectation but also with high probability.Our starting point is the state-of-The-Art randomized algorithm for maintaining a maximal matching (Solomon, FOCS'16). We carefully build on the approach of Solomon, but, due to inherent differences between the maximal matching and (Δ+1)-coloring problems, we need to deviate significantly from it in several crucial and highly nontrivial points.1
AB - The problem of (Δ+1)-vertex coloring a graph of maximum degree Δhas been extremely well studied over the years in various settings and models. Surprisingly, for the dynamic setting, almost nothing was known until recently. In SODA'18, Bhattacharya, Chakrabarty, Henzinger and Nanongkai devised a randomized algorithm for maintaining a (Δ+1)-coloring with O(log ") expected amortized update time. In this article, we present an improved randomized algorithm for (Δ+1)-coloring that achieves O(1) amortized update time and show that this bound holds not only in expectation but also with high probability.Our starting point is the state-of-The-Art randomized algorithm for maintaining a maximal matching (Solomon, FOCS'16). We carefully build on the approach of Solomon, but, due to inherent differences between the maximal matching and (Δ+1)-coloring problems, we need to deviate significantly from it in several crucial and highly nontrivial points.1
KW - Graph coloring
KW - dynamic graph algorithms
UR - http://www.scopus.com/inward/record.url?scp=85128271484&partnerID=8YFLogxK
U2 - 10.1145/3494539
DO - 10.1145/3494539
M3 - מאמר
AN - SCOPUS:85128271484
VL - 18
JO - ACM Transactions on Algorithms
JF - ACM Transactions on Algorithms
SN - 1549-6325
IS - 2
M1 - 10
ER -