An iterative algorithm of computing the transitive closure of a union of parameterized affine integer tuple relations

Authors:
Bielecki Wlodzimierz;Klimek Tomasz;Palkowski Marek;Anna Beletska
Affiliations:
Technical University of Szczecin, Szczecin, Poland;Technical University of Szczecin, Szczecin, Poland;Technical University of Szczecin, Szczecin, Poland;INRIA Saclay, Parc Club Universite, Orsay Cedex, France
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Year:
2010

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Abstract

A novel iterative algorithm of calculating the exact transitive closure of a parameterized graph being represented by a union of simple affine integer tuple relations is presented. When it is not possible to calculate exact transitive closure, the algorithm produces its upper bound. To calculate the transitive closure of the union of all simple relations, the algorithm recognizes the class of each simple relations, calculates its exact transitive closure, forms the union of calculated transitive closures, and applies this union in an iterative procedure. Results of experiments aimed at the comparison of the effectiveness of the presented algorithm with those of related ones are outlined and discussed.