^{1} Department of Computer Science, Faculty of Science, Aarhus University, Aarhus University^{2} Department of Computer Science, Science and Technology, Aarhus University^{3} KU Leuven^{4} Department of Computer Science, Science and Technology, Aarhus University

DOI:

10.1007/978-3-642-31113-0_8

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

Type:

Conference paper

Language:

English

Published in:

Lecture Notes in Computer Science, 2012, Vol 7342, p. 132-156

Main Research Area:

Science/technology

Publication Status:

Published

Review type:

Peer Review

Conference:

International Conference on the Mathematics of Program ConstructionMathematics of Program Construction, 2012