A Lower Bound for the Shortest Path Problem

Authors:
Ketan Mulmuley;Pradyut Shah
Affiliations:
-;-
Venue:
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Year:
2000

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Cited 1

On the complexity of time-dependent shortest paths

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms

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Abstract

We show that the Shortest Path Problem cannot be solved in o(log n) time on an unbounded fan-in PRAM without bit operations using poly (n) processors even when the bit-lengths of the weights on the edges are restricted to be of size O(log3 n). This shows that the matrix-based repeated squaring algorithm for the Shortest Path Problem is optimal in the unbounded fan-in PRAM model without bit operations.