TY  - JOUR
A1  - Höfner, Peter
A1  - Möller, Bernhard
T1  - Dijkstra, Floyd and Warshall meet Kleene
T2  - Formal Aspects of Computing
N2  - 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.
KW  - Theoretical Computer Science
KW  - Software
Y1  - 2012
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/58760
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-587605
SN  - 0934-5043
SN  - 1433-299X
VL  - 24
IS  - 4-6
SP  - 459
EP  - 476
PB  - Springer Science and Business Media LLC
ER  -