Processor efficient parallel graph algorithms
Year: 2015
Type: dissertation
Abstract: Several parallel algorithms are presented. The following results were achieved: (1) An optimal randomized parallel algorithm for finding connected components in undirected graphs. The algorithm takes O(log(n)) time. (2) A parallel BFS algorithm for directed graphs that improves the number of processors required for BFS of a directed graph. Our algorithm requires O(log$\sp2(n)$) time using ${M(n)}\over{{\rm log}(n)}$ processors where $M(n)$, is the number of operations for matrix multiplication over the ring of the integers. The previously best known result requires $O(n\sp3$ log(n)) operations. The value of $M(n)$, bounded below by $n\sp2$ is successively being improved, and currently stands at $n\sp{2.376}$ (7). (3) Improvement of the $\sqrt{6n}$ Djidjev (8) sequential separator algorithm. Our separator size is ${7\over3}\sqrt{n}$. The previously best known result is $\sqrt{6n}$ (8). (4) A parallel algorithm for an $O(\sqrt{n})$ separator in planar graph which uses $O(n\sp{1+\epsilon})$ processors and O(log$\sp2(n)$) time. (Copies available exclusively from Micrographics Department, Doheny Library, USC, Los Angeles, CA 90089-0182.)
Author: Gazit, Hillel (author)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2266665304