Abstract
We design centralized local algorithms for: maximal independent set, maximal matching, and graph coloring. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes is O(log* n), where n is the number of vertices of the input graph. Our algorithms for maximal independent set and maximal matching improves over previous randomized algorithms by Alon et al. (SODA 2012) and Mansour et al. (ICALP 2012). In these previous algorithms, the number of probes and the space required for storing the state between queries are poly(logn).
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