Uniform Linked Lists Contraction
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We present a parallel algorithm (EREW PRAM algorithm) for linked lists contraction. We show that when we contract a linked list from size n to size n/c for a suitable constant c we can pack the linked list into an array of size n/d for a constant 1 < d≤ c in the time of 3 coloring the list. Thus for a set of linked lists with a total of n elements and the longest list has l elements our algorithm contracts them in O(nlog i/p+(log^(i)n+log i )loglog l+ log l) time, for an arbitrary constructible integer i, with p processors on the EREW PRAM, where log^(1) n =log n and log^(t)n=loglog^(t-1) n and log^*n=min{ i|log^(i) n < 10}. When i is a constant we get time O(n/p+log^(i)nloglog l+log l). Thus when l=Ω (log^(c)n) for any constant c we achieve O(n/p+log l) time. The previous best deterministic EREW PRAM algorithm has time O(n/p+log n) and best CRCW PRAM algorithm has time O(n/p+log n/loglog n+log l). Keywords: Parallel algorithms, linked list, linked list contraction, uniform linked list contraction, EREW PRAM.
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