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.
| Originalsprog | Engelsk |
|---|---|
| Titel | Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings |
| Redaktører | Jeremy Gibbons, Pablo Nogueira |
| Antal sider | 25 |
| Forlag | Springer VS |
| Publikationsdato | 1. jan. 2012 |
| Sider | 132-156 |
| ISBN (Trykt) | 9783642311123 |
| Status | Udgivet - 1. jan. 2012 |
| Begivenhed | 11th International Conference on Mathematics of Program Construction, MPC 2012 - Madrid, Spanien Varighed: 25. jun. 2012 → 27. jun. 2012 |
Konference
| Konference | 11th International Conference on Mathematics of Program Construction, MPC 2012 |
|---|---|
| Land | Spanien |
| By | Madrid |
| Periode | 25/06/2012 → 27/06/2012 |
| Navn | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Vol/bind | 7342 LNCS |
| ISSN | 0302-9743 |
Fingeraftryk
Citer dette
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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-proceeding › Konferencebidrag i proceedings › Forskning › peer review
TY - GEN
T1 - Calculating graph algorithms for dominance and shortest path⋆
AU - Sergey, Ilya
AU - Midtgaard, Jan
AU - Clarke, Dave
PY - 2012/1/1
Y1 - 2012/1/1
N2 - 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.
AB - 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.
KW - Dominance
KW - Fixed-point calculus
KW - Fixed-point fusion
KW - Galois connections
KW - Graph algorithms
KW - Shortest path algorithm
UR - http://www.scopus.com/inward/record.url?scp=84900034962&partnerID=8YFLogxK
M3 - Article in proceedings
AN - SCOPUS:84900034962
SN - 9783642311123
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 132
EP - 156
BT - Mathematics of Program Construction - 11th International Conference, MPC 2012, Proceedings
A2 - Gibbons, Jeremy
A2 - Nogueira, Pablo
PB - Springer VS
ER -