The power of parallel prefix
TL;DR: This study assumes the weakest PRAM model, where shared memory locations can only be exclusively read or written (the EREW model) to solve the prefix computation problem, when the order of the elements is specified by a linked list.
Abstract: The prefix computation problem is to compute all n initial products a1* . . . *a1,i=1, . . ., n of a set of n elements, where * is an associative operation. An O(((logn) log(2n/p))XI(n/p)) time deterministic parallel algorithm using p≤n processors is presented to solve the prefix computation problem, when the order of the elements is specified by a linked list. For p≤O(n1-e)(e〉0 any constant), this algorithm achieves linear speedup. Such optimal speedup was previously achieved only by probabilistic algorithms. This study assumes the weakest PRAM model, where shared memory locations can only be exclusively read or written (the EREW model).
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TL;DR: A family of parallel algorithms solving the prefix problem on the combinational circuit model is presented, and the new prefix circuits are waist-size optimal with waist 1 (WSO-1) and are the fastest among all WSO- 1 prefix circuits of the same width and fan-out.
11 citations
TL;DR: An O(log n) time parallel algorithm with O( n log n ) processors on the EREW PRAM for constructing a spanning tree on an unweighted permutation graph.
11 citations
01 Jul 1992
TL;DR: This paper presents an optimal parallel algorithm for solving the problem of detecting the weak visibility of an n-vertex simple polygon and identifies every edge from which P is weakly visible.
Abstract: The problem of detecting the weak visibility of an n-vertex simple polygon P is that of finding whether or not P is weakly visible from one of its edges and (if it is) identifying every edge from which P is weakly visible. In this paper, we present an optimal parallel algorithm for solving this problem. Our algorithm runs in O(log n) time using O(n/log n) processors in the CREW-PRAM computational model, and is very different from the sequential algorithms for this problem. This algorithm also enables us to optimally solve, in parallel, several other problems on weakly visible polygons.
10 citations
05 Jun 1989
TL;DR: This work presents a parallel algorithm for computing the visible portion of a simple polygonal chain with n vertices from a point in the plane that is asymptomatically optimal in the CREW-PRAM computational model.
Abstract: We present a parallel algorithm for computing the visible portion of a simple polygonal chain with n vertices from a point in the plane The algorithm runs in O(log n) time using O(n/ log n) processors in the CREW-PRAM computational model, and hence is asymptomatically optimal
10 citations
01 Jan 1987
TL;DR: This paper completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices.
Abstract: The prefix problem consists of computing all the products x0x1…xj (j=0, …, N - 1), given a sequence x = (x0, x1, …, xN - 1) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by S and T size and computation time, respectively, we have S = T((N/T) log(N/T)), for non-cycle-free semigroups, and S = T(N/T), for cycle-free semigroups. In both cases, T ∈ [O(logN), O(N)].
10 citations