AN ITERATIVE ALGORITHM OF COMPUTING THE TRANSITIVE CLOSURE OF A UNION OF PARAMETRIZED AFFINE INTEGER TUPLE RELATIONS-Reference-Cited by-同舟云学术

AN ITERATIVE ALGORITHM OF COMPUTING THE TRANSITIVE CLOSURE OF A UNION OF PARAMETRIZED AFFINE INTEGER TUPLE RELATIONS

Published:2012-03 Issue:01 Volume:04 Page:1250011
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

BIELECKI WLODZIMIERZ¹,KLIMEK TOMASZ¹,PALKOWSKI MAREK¹,BELETSKA ANNA²

Affiliation:

1. Technical University of Szczecin, ul. Zolnierska 49, Szczecin, Poland

2. INRIA Saclay, Parc Club Universite, 3, rue J. Rostand, 91893 Orsay Cedex, France

Abstract

A novel iterative algorithm of calculating the exact transitive closure of a parametrized 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830912500115

Reference3 articles.

1. Calculating Exact Transitive Closure for a Normalized Affine Integer Tuple Relation

2. W. Kelly, Transitive Clousure of Infinite Graphs and its Applications, Languages and Compilers for Parallel Computing (Springer, 1996) pp. 126–140.