Abstract
The problem of computing maximal independent sets in graphs on parallel models of computation has received considerable attention. We present simple efficient parallel algorithms for the maximal independent set problem—and a relaxation that we call the fractional independent set problem—restricted to planar graphs. Our algorithms rely on an efficient parallel algorithm for constructing large independent sets in graphs of bounded degree. The latter is accomplished by a simple reduction to the same problem for lists. Using a linear number of EREW processors, the algorithm identifies a maximal independent set in an arbitrary planar graph in O( logn log∗n) parallel time. A randomized version of the algorithm runs in O(log n) expected parallel time.
Published Version
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