We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated 2 ^O(√logn)-time algorithm of Panconesi and Srinivasan [STOC’92] and settles a central and long-standing question in distributed graph algorithms. It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other problems, hence resolving several well-known and decades-old open problems, including Linial’s question about the deterministic complexity of maximal independent set [FOCS’87; SICOMP’92]—which had been called the most outstanding problem in the area.

The main implication is a more general distributed derandomization theorem: Put together with the results of Ghaffari, Kuhn, and Maus [STOC’17] and Ghaffari, Harris, and Kuhn [FOCS’18], our network decomposition implies that P-RLOCAL = P-LOCAL.

That is, for any problem whose solution can be checked deterministically in polylogarithmic-time, any polylogarithmic-time randomized algorithm can be derandomized to a polylogarithmic-time deterministic algorithm. Informally, for the standard first-order interpretation of efficiency as polylogarithmic-time, distributed algorithms do not need randomness for efficiency.

By known connections, our result leads also to substantially faster randomized distributed algorithms for a number of well-studied problems including (Δ+1)-coloring, maximal independent set, and Lovász Local Lemma, as well as massively parallel algorithms for (Δ+1)-coloring.