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## Convex Geometry and Semiflows in P/T Nets. A Comparative Study of Algorithms for Computation of Minimal P-Semiflows.

Colom, J.M.;
Silva, M.
In:
*Proceedings of the 10th International Conference on Application and Theory of Petri Nets, 1989, Bonn, Germany*, pages 74-95.
1989.

Also:
Universidad de Zaragoza, departamento de ingenieria electrica e informatica, Research Report 89-01,
January 1989.

Also in:
Rozenberg, G.: *Lecture Notes in Computer Science, Vol. 483; Advances in Petri Nets 1990*, pages 79-112.
Berlin, Germany: Springer-Verlag,
1991.

Abstract:
P-semiflows are nonnegative left annullers of a net's flow matrix. The
concept of minimal p-semiflow is known in the context of mathematical
programming under the name `extremal direction of a cone'. The algorithms
known in the domain of P/T nets for computing elementary semi-flows are
basically improvements of the basic Fourier-Motzkin method. One of the
fundamental problems of these algorithms is their complexity. Various
methods and rules for mitigating this problem are examined. As a result,
the paper presents two improved algorithms which are more efficient and
robust when handling `real-life' nets.

Keywords:
convex geometry (and) semiflows (in) place/transition net(s); minimal
p-semiflows computation; Fourier-Motzkin method; complexity reduction.

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