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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Calculating Graph Algorithms for Dominance and Shortest Path
verfasst von : Ilya Sergey, Jan Midtgaard, Dave Clarke
Erschienen in: Mathematics of Program Construction
Verlag: Springer Berlin Heidelberg
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We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by
fixed-point fusion
of (1) a least fixed point expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length.
The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation.