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Calculating Graph Algorithms for Dominance and Shortest Path

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Authors:
  • Sergey, Ilya ;
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    Department of Computer Science, Faculty of Science, Aarhus University, Aarhus University
  • Midtgaard, Jan ;
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    Department of Computer Science, Science and Technology, Aarhus University
  • Clarke, Dave
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    KU Leuven
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
Submission year:
2012
Scientific Level:
Scientific
ID:
2185898816

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