A Lower Bound for the Shortest Path Problem

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.

• Type: Conference
• Year: 2000
• Where: COCO
• Authors: Ketan Mulmuley, Pradyut Shah
• Keywords: Algorithms, Bit Operations, COCO 2000, Shortest Path Problem, Unbounded Fan-in Pram