Abstract
Given a set of n circular arcs, the problem of finding a minimum number of circular arcs whose union covers the whole circle has been considered both in sequential and parallel computational models. Here we present a parallel algorithm in the EREW PRAM model that runs in O(log n) time using O( n) processors if the arcs are not given already sorted, and using O( n/log n) processors otherwise. Our algorithm is optimal since the problem has an Ω( n log n) lower bound for the unsorted-arcs case, and an Ω( n) lower bound for the sorted-arcs case. The previous best known parallel algorithm runs in O(log n) time using O( n 2) processors, in the worst case, in the CREW PRAM model.
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