Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations
Year: 1980
Type: conference-paper
Abstract: Any Boolean straight-line program which computes the transitive closure of an nxn Boolean matrix by successive squaring requires time exceeding any polynomial in n if the space used is o(n). This is the first demonstration of a “natural” algorithm which (1) has a polynomial time implementation and (2) has a small (e.g., O(log2n)) space implementation, but (3) has no implementation running in polynomial time and small space simultaneously. It is also shown that any implementation of Warshall's transitive closure algorithm requires Ω(n) space.
Author: Martin Tompa
Institution: University of Washington
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2164840273