Fast and efficient solution of path algebra problems
Victor Y. Pan,John H. Reif +1 more
TLDR
A class of new applications of the nested dissection method is presented, this time to path algebra computations, where the path algebra problem is defined by a symmetric matrix A whose associated undirected graph G has a known family of separators of small size s ( n ) (in many cases of interest).About:
This article is published in Journal of Computer and System Sciences.The article was published on 1989-06-01 and is currently open access. It has received 43 citations till now.read more
Citations
More filters
Proceedings ArticleDOI
Faster shortest-path algorithms for planar graphs
TL;DR: The shortest-path algorithm yields an $O(n^{4/3} \log n)$-time algorithm for finding a perfect matching in a planar bipartite graph and a similar improvement is obtained for maximum flow in a directed planar graph.
Journal ArticleDOI
Complexity of computations with matrices and polynomials
TL;DR: The complexity of polynomial and matrix computations, as well as their various correlations to each other and some major techniques for the design of algebraic and numerical algorithms are reviewed.
Journal ArticleDOI
Fast and efficient parallel solution of sparse linear systems
Victor Y. Pan,John H. Reif +1 more
TL;DR: The algorithm computes a recursive factorization of A such that the solution of any other linear system A requires only time and the number of processors sufficient for multiplying two rational matrices in time.
Journal ArticleDOI
Efficient parallel algorithms for computing all pair shortest paths in directed graphs
TL;DR: This work presents parallel algorithms for computing all pair shortest paths in directed graphs and has time complexityO(n3/p+logn) on the PRAM usingp processors.
Proceedings ArticleDOI
A linear-processor polylog-time algorithm for shortest paths in planar graphs
TL;DR: An algorithm requiring polylog time and a linear number of processors to solve single-source shortest paths in directed planar graphs, bounded-genus graphs, and 2-dimensional overlap graphs is given.
References
More filters
Journal ArticleDOI
Algorithm 97: Shortest path
TL;DR: The procedure was originally programmed in FORTRAN for the Control Data 160 desk-size computer and was limited to te t ra t ion because subroutine recursiveness in CONTROL Data 160 FORTRan has been held down to four levels in the interests of economy.
Journal ArticleDOI
On a routing problem
TL;DR: Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, the functional equation technique of dynamic programming and approximation in policy space yield an iterative algorithm which converges after at most (N-1) iterations.
Journal ArticleDOI
A Separator Theorem for Planar Graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A, B, C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than ${2n/3}$ vertices, and C contains no more than $2.
A separator theorem for planar graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A,B,C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than $2.