A New Technique For Distributed Symmetry Breaking

摘要

We introduce Multi-Trials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color trade-off. To get a A + 1 coloring takes time O(logΔ + log n~(2/1)). To obtain an O(A + log~(1+1/log~*n n) n) coloring takes time O(log* n). This is more than an exponential improvement in time for graphs of polylogarithmic degree. Our fastest algorithm works in constant time using O(Δ log~(c) n + log~(1+1c) n) colors, where c denotes an arbitrary constant and log~(c) n denotes the c times (recursively) applied logarithm to n. We also use the Multi-Trials technique to compute network decompositions and to compute maximal independent set (MIS), obtaining new results for several graph classes.