Calculating graph algorithms for dominance and shortest path

Ilya Sergey, Jan Midtgaard, Dave Clarke

Publikation: Bidrag til bog/antologi/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review

Resumé

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.

OriginalsprogEngelsk
TitelMathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings
RedaktørerJeremy Gibbons, Pablo Nogueira
Antal sider25
ForlagSpringer VS
Publikationsdato1. jan. 2012
Sider132-156
ISBN (Trykt)9783642311123
StatusUdgivet - 1. jan. 2012
Begivenhed11th International Conference on Mathematics of Program Construction, MPC 2012 - Madrid, Spanien
Varighed: 25. jun. 201227. jun. 2012

Konference

Konference11th International Conference on Mathematics of Program Construction, MPC 2012
LandSpanien
ByMadrid
Periode25/06/201227/06/2012
NavnLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Vol/bind7342 LNCS
ISSN0302-9743

Fingeraftryk

Directed graphs
Fusion reactions
Polynomials

Citer dette

Sergey, I., Midtgaard, J., & Clarke, D. (2012). Calculating graph algorithms for dominance and shortest path. I J. Gibbons, & P. Nogueira (red.), Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings (s. 132-156). Springer VS. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind. 7342 LNCS
Sergey, Ilya ; Midtgaard, Jan ; Clarke, Dave. / Calculating graph algorithms for dominance and shortest path. Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings. red. / Jeremy Gibbons ; Pablo Nogueira. Springer VS, 2012. s. 132-156 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 7342 LNCS).
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Sergey, I, Midtgaard, J & Clarke, D 2012, Calculating graph algorithms for dominance and shortest path. i J Gibbons & P Nogueira (red), Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings. Springer VS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), bind 7342 LNCS, s. 132-156, 11th International Conference on Mathematics of Program Construction, MPC 2012, Madrid, Spanien, 25/06/2012.

Calculating graph algorithms for dominance and shortest path. / Sergey, Ilya; Midtgaard, Jan; Clarke, Dave.

Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings. red. / Jeremy Gibbons; Pablo Nogueira. Springer VS, 2012. s. 132-156 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 7342 LNCS).

Publikation: Bidrag til bog/antologi/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review

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Sergey I, Midtgaard J, Clarke D. Calculating graph algorithms for dominance and shortest path. I Gibbons J, Nogueira P, red., Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings. Springer VS. 2012. s. 132-156. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 7342 LNCS).