Graphs and algorithms
How to multiply matrices faster
How to multiply matrices faster
Finding small simple cycle separators for 2-connected planar graphs
Journal of Computer and System Sciences
A Unified Approach to Path Problems
Journal of the ACM (JACM)
Fast Algorithms for Solving Path Problems
Journal of the ACM (JACM)
Communications of the ACM
Parallel algorithms for minimum cuts and maximum flows in planar networks
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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This paper extends the authors' parallel nested dissection algorithm of [13] originally devised for solving sparse linear systems. We present a class of new applications of the nested dissection method, this time to path algebra computations (in both cases of single source and all pair paths), where the path algebra problem is defined by a symmetric matrix A whose associated graph G with n vertices is planar. We substantially improve the known algorithms for path algebra problems of that general class; this has further applications to maximum flow and minimum cut problems in an undirected planar network and to the feasibility testing of a multicommodity flow in a planar network.