An introduction to parallel algorithms
An introduction to parallel algorithms
Journal of Systems and Software - Special issue on software engineering for distributed computing
An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations
Journal of the ACM (JACM)
A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
IEEE Transactions on Computers
Efficient parallel solutions of linear algebraic circuits
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Parallel Processing of First Order Linear Recurrence on SMP Machines
The Journal of Supercomputing
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A new type of recurrence equations called "indexed recurrences" (IR) is defined, in which the common notion of X[i] = op(X[i],X[i-1]) i=1..n is generalized to X[g(i)] = op(X[f(i)],X[h(i)]) f,g,h:{1..n} - {1..m}. This enables us to model sequential loops of the form for i = 1 to n do begin X[g(i)] := op(X[f(i)],X[h(i)]); as IR equations.Thus, a parallel algorithm that solves a set of IR equations is in fact a way to transform sequential loops into parallel ones. Note that the circuit evaluation problem (CVP) can also be expressed as a set of IR equations. Therefore an efficient parallel solution to the general IR problem is not likely to be found, as such solution would also solve the CVP, showing that P is a subset of, or equal NC.In this paper we introduce parallel algorithms for two variants of the IR equations problem: 1. An O(log n) greedy algorithm for solving IR equations where g(i) is distinct and h(i) = g(i) using O(n) processors.2. An O(log^2 n) algorithm with no restriction on f,g or h, using up to O(n^2) processors.However, we show that for general IR, 'op' must be commutative so that a parallel computation can be used.