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A polynomial ideal membership problem is an (n+1)-tuple P = 〈p, p1, p2,..., pn〉 where p and the pi are multivariate polynomials over some ring, and the problem is to determine whether p is in the ideal generated by the pi. For polynomials over the integers or rationals,...
We present a parallel algorithm for the two processor scheduling problem. This algorithm constructs an optimal schedule for unit execution time task systems with arbitrary precedence constraints using a polynomial number of processors and running in time polylog in the size of the input. Whereas previous parallel solutions for the problem made extensive use of randomization, our algorithm is completely...
We combine a parallel algorithm for the two processor scheduling problem, which runs in polylog time on a polynomial number of processors, with an algorithm to find transitive orientations of graphs where they exist. Both algorithms together solve the maximum clique problem and the minimum coloring problem for comparability graphs, and the maximum matching problem for co-comparability graphs. These...
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