An Optimal Parallel Algorithm for the Minimum Circle-Cover Problem

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 Iuns in O(logn) time using O(n) processors if the arcs are not given already sorted, and using Den/logn) processors otherwise. OUI algorithm is optimal since the problem has an n(nlogn) lower hound for the unsorted arcs case, and an n(n) lower bound for the sorted arcs case. The previous best known parallel algorithm runs in O(logn) time using O(n:!) processors, in the worst case, in the CREW PRAM model.