### 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

^{⋆}. 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

}

^{⋆}. 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.

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 -

^{⋆}. 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).