HAL: hal-00374984, version 1
 MEMICS 2007: Third Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, Znojmo : Tchèque, République (2007)
 An Efficient Algorithm for the Computation of Optimum Paths in Weighted Graphs
 Marius Bozga 1, Radu Iosif 1
 (2007-10-26)
 The goal of this paper is to identify a more efficient algorithm for the computation of the path of minimum ratio (i.e. the quotient of the weight divided by the length) in a weighted graph. The main application of this technique is to improve the efficiency of reachability analysis for flat counter automata with Difference Bound Matrix constraints on transitions. A previous result showed that these paths could be defined using Presburger arithmetic. However, this method is costly, as the complexity of deciding satisfiability of Presburger formulae has a double exponential lower bound. Our solution avoids the use of Presburger arithmetic, by computing the function between any $n \in \Nat$ and the weight of the minimal path of length $n$. The function is computed iteratively, by computing the minimal fixed point of a system of set constraints, involving semilinear sets. This requires a min operator on linear sets, which is implemented using rewrite rules.
 1: VERIMAG (VERIMAG - IMAG) CNRS : UMR5104 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
 Subject : Computer Science/Embedded Systems
 Keyword(s): weighted graphs – minimal paths – Presburger arithmetic – policy iteration
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 hal-00374984, version 1 http://hal.archives-ouvertes.fr/hal-00374984 oai:hal.archives-ouvertes.fr:hal-00374984 From: Marius Bozga <> Submitted on: Friday, 10 April 2009 16:02:10 Updated on: Friday, 10 April 2009 16:15:32