The purpose of this paper is a study of computation that can be done locally in a distributed network. By locally we mean within time (or distance) independent of the size of the network. I n particular we are interested in algorithms that are robust, i.e., perform well even if the underlying gmph is not stable and links continuously fail and come-up. W e introduce and study the happy coloring & orientation problem and show that it yields a robust local solution to the (d, m)-dining philosophers problem of Naor and Stoclnneyer 1171. This problem is similar to the usual dining philosophers problem, ezcept that each philosopher has access to d forks but needs only m of them to eat. W e give a robust local solution if m 5 [d/21 (necessity of this inequality for any local solution was known previously).Two other problems we investigate are: ( I ) the amount of initial s y m m e t r y -b d n g needed to solve certain problems locally (for example, our algorithms need considembly less s y m m e t r y -b d n g than having a unique ID on each node), and (2) the single-step color reduction problem: given a coloring with c colors of the nodes of a gmph, what is the smallest number of colors c' such that every node can recolor itself with one of c' colors as a function of its immediate neighborhood only. . Part of this work waa done while at IBM Almaden Rasesreh Center. Resesrch supported by an Alon Fellowship and by an Israel-France grant.