An Optimal Distributed $(\Delta+1)$-Coloring Algorithm?
نویسندگان
چکیده
Vertex coloring is one of the classic symmetry breaking problems studied in distributed com-puting. In this paper we present a new algorithm for (∆ + 1)-list coloring in the randomizedLOCAL model running in O(log n + Detd(poly logn)) time, where Detd(n ′) is the determinis-tic complexity of (deg+1)-list coloring (v’s palette has size deg(v) + 1) onn′-vertex graphs.This improves upon a previous randomized algorithm of Harris, Schneider, and Su [18] withcomplexity O(√log∆ + log log n + Detd(poly logn)), and is dramatically faster than the bestknown deterministic algorithm of Fraigniaud, Heinrich, and Kosowski [14], with complexityO(√∆ log ∆+ log n).Our algorithm appears to be optimal. It matches the Ω(log n) randomized lower bound,due to Naor [25] and sort of matches the Ω(Det(poly logn)) randomized lower bound due toChang, Kopelowitz, and Pettie [7], where Det is the deterministic complexity of (∆ + 1)-listcoloring. The best known upper bounds on Detd(n ′) and Det(n′) are both 2√logn) (Panconesiand Srinivasan [26]) and it is quite plausible that the complexities of both problems are thesame, asymptotically. ∗This work is supported by NSF grants CCF-1514383 and CCF-1637546.
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