Early Computer Science Adventures of a Mathematician
Part of the
Discrete Mathematics and Theoretical Computer Science
book series (DISCMATH)
I had several experiences involving computer science before I knew that it was what I was doing. The first of these took place when I was visiting the Institute for Advanced Study during the two years 1957–59. Larry Wilets, a professor of physics at the University of Washington, asked me to help him with the many calculations he needed to make in order to find the eigenvalues of a sparse binary matrix which arose from his observed data in experimental physics. He challenged me to find a graph theoretic method which would save him enormous amounts of time. I was pleasantly surprised when I solved this problem with a matrix algorithm for finding the strongly connected components of a digraph. Later I learned that in 1962 a paper was published which presented “Warshall’s Algorithm”. He had published his paper in a computer journal whereas mine appeared in the Journal of Mathematical Physics . That is why the determination of the transitive closure of a binary relation is attributed to him. In 1962, I applied this method to the inversion of a sparse matrix . Gabriel Kron visited me at University of Michigan to tell me about his “method of tearing” which utilizes the same method for matrix inversion. His work preceded mine.
KeywordsInformation Retrieval Transitive Closure Theoretical Computer Science Acyclic Digraph Span Tree Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
A.J. Schwenk, F. Harary. Efficiency of dissemination of information in one-way and two-way communication networks. Behavioral Sci
. 19 (1974) 133–135.CrossRefGoogle Scholar
A.J. Schwenk, F. Harary. The communication problem on graphs and digraphs. J. Franklin Institute
297 (1974) 491–495.MathSciNetMATHCrossRefGoogle Scholar
F. Buckley. F. Harary. Distance in Graphs
. Addison-Wesley, Reading (1990).MATHGoogle Scholar
F. Harary. A graph theoretic method for the complete reduction of a matrix with a view toward finding its eigenvalues. Math. Physics
38 (1959) 104–111.MATHGoogle Scholar
F. Harary. Graph theoretic methods in the management sciences. Management Sci
. 5 (1959) 387–403.MathSciNetMATHCrossRefGoogle Scholar
F. Harary. Graph theoretic models. Theoret. Comput. Sci.
11 (1980) 117–121.MathSciNetMATHCrossRefGoogle Scholar
F. Harary. On the consistency of precedence matrices. J. Assoc. Comput. Mach.
7 (1960) 255–259.MathSciNetMATHGoogle Scholar
F. Harary. A graph theoretic approach to matrix inversion by partitioning. Numer. Math.
4 (1962) 128–135.MathSciNetMATHCrossRefGoogle Scholar
F. Harary. Graph Theory
. Addison-Wesley, Reading MA (1969).Google Scholar
F. Harary, D. Hsiao. A formal system for information retrieval from files. Comm. Assoc. Comput. Mach.
13 (1970) 67–73.MATHGoogle Scholar
F. Harary. E.M. Palmer. Graphical Enumeration
. Academic Press, New York (1975).Google Scholar
© Springer-Verlag London Limited 2001