Lower bounds for solving linear diophantine equations on random access machines
Journal of the ACM (JACM)
A taxonomy of problems with fast parallel algorithms
Information and Control
New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P
IEEE Transactions on Computers
Gaussian elimination with pivoting is P-complete
SIAM Journal on Discrete Mathematics
A complexity theory of efficient parallel algorithms
Theoretical Computer Science - Special issue: Fifteenth international colloquium on automata, languages and programming, Tampere, Finland, July 1988
Introduction to algorithms
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
A Theory of Strict P-completeness
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
On the parallel complexity of matrix factorization algorithms
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
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Consider the problem of determining the pivot sequence used by the Gaussian Elimination algorithm with Partial Pivoting (GEPP). Let N stand for the order of the input matrix and let &egr; be any positive constant. Assuming P ≠ NC, we prove that if GEPP were decidable in parallel time M1/2–&egr; then all the problems in P would be characterized by polynomial speedup. This strengthens the P-completeness result that holds of GEPP. We conjecture that our result is valid even with the exponent 1 replaced for 1/2, and provide supporting arguments based on our result. This latter improvement would demonstrate the optimality of the naive parallel algorithm for GEPP (modulo P ≠ NC).