Dijkstra, Floyd and Warshall meet Kleene
- Around 1960, Dijkstra, Floyd and Warshall published papers on algorithms for solving single source and all-sources shortest path problems, respectively. These algorithms, nowadays named after their inventors, are well known and well established. This paper sheds an algebraic light on these algorithms. We combine the shortest path problems with Kleene algebra, also known as Conway's regular algebra. This view yields a purely algebraic version of Dijkstra's shortest path algorithm and the one by Floyd/Warshall. Moreover, the algebraic abstraction yields applications of these algorithms to structures different from graphs and pinpoints the mathematical requirements on the underlying cost algebra that ensure their correctness.
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| Author: | Peter Höfner, Bernhard MöllerGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-587605 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/58760 |
| ISSN: | 0934-5043OPAC |
| ISSN: | 1433-299XOPAC |
| Parent Title (English): | Formal Aspects of Computing |
| Publisher: | Springer Science and Business Media LLC |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2012 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2019/07/23 |
| Tag: | Theoretical Computer Science; Software |
| Volume: | 24 |
| Issue: | 4-6 |
| First Page: | 459 |
| Last Page: | 476 |
| DOI: | https://doi.org/10.1007/s00165-012-0245-4 |
| Institutes: | Fakultät für Angewandte Informatik |
| Fakultät für Angewandte Informatik / Institut für Informatik | |
| Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
| Licence (German): |  Deutsches Urheberrecht |
