@inproceedings{6da75e25a82c4c1facec0bf806f534fe,

title = "Calculating graph algorithms for dominance and shortest path⋆",

abstract = "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.",

keywords = "Dominance, Fixed-point calculus, Fixed-point fusion, Galois connections, Graph algorithms, Shortest path algorithm",

author = "Ilya Sergey and Jan Midtgaard and Dave Clarke",

year = "2012",

month = jan,

day = "1",

language = "English",

isbn = "9783642311123",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer VS",

pages = "132--156",

editor = "Jeremy Gibbons and Pablo Nogueira",

booktitle = "Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings",

note = "11th International Conference on Mathematics of Program Construction, MPC 2012 ; Conference date: 25-06-2012 Through 27-06-2012",

}