Dynamic Algorithms for Graph Coloring
Sayan Bhattacharya, Deeparnab Chakrabarty, Monika Rauch Henzinger, Danupon Nanongkai · Society for Industrial and Applied Mathematics eBooks · 2018
We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for (Δ + 1)- vertex coloring and (2Δ – 1)-edge coloring in a graph with maximum degree Δ. It is natural to ask if we can efficiently maintain such colorings in the dynamic setting as well. We get the following three results. (1) We present a randomized algorithm which maintains a (Δ + 1)-vertex coloring with O(log Δ) expected amortized update time. (2) We present a deterministic algorithm which maintains a (1 + o(1)Δ-vertex coloring with O(polylog Δ) amortized update time. (3) We present a simple, deterministic algorithm which maintains a (2Δ – 1)-edge coloring with O(log Δ) worst-case update time. This improves the recent O(Δ)-edge coloring algorithm with worst-case update time [4].