A Preflow Approach to Maximum Flows in Parametric Networks Applied to Assessing the Legal Information

  • Livia Sangeorzan Transilvania University of Brasov Faculty of Mathematics and Informatics B-dul Eroilor 29, 500036, Brasov, Romania
  • Mircea Parpalea National College Andrei Şaguna of Brasov 1, Şaguna, street, 590000, Brasov, Romania
  • Mihaela Marinela Parpalea Transilvania University of Brasov Faculty of Letters 25, Eroilor, Blvd, 500030, Brasov, Romania
  • Angela Repanovici Transilvania University of Brasov Faculty of Product Design and Environment 25, Eroilor, Blvd, 500030, Brasov, Romania
  • Roxana Matefi Transilvania University of Brasov Faculty of Law 25, Eroilor, Blvd, 500030, Brasov, Romania
  • Ioana Nicolae Transilvania University of Brasov Faculty of Law 25, Eroilor, Blvd, 500030, Brasov, Romania

Abstract

The present paper proposes a fractal-like approach to the parametric flow problem, derived from the rules and recursion of generative linguistics. In the same manner in which any sentence can be analysed in terms of "theme" of the sentence (that which is spoken about in the sentence) and "rheme" of the sentence (that which is said about the theme in the sentence), in the proposed parametric preflow-push algorithm, a "partitioning push" (a non-cancelling push of flow in the parametric residual network) might leave the node unbalanced for only a subinterval of the range of parameter values. This will lead to separating the problem for the two disjoints subintervals, which allows the algorithm to continue after the same rules, independently, on each of the partitioned subintervals. The algorithm runs as the template-like structure of a dialogue act which reveals a design where information about the items (part-of-speech) is a two sections vector with one segment for each of the used part of speech categories. The article also proposes a possible application of the algorithm in assessing legal information and in semantic evaluation of legislation.

Author Biography

Livia Sangeorzan, Transilvania University of Brasov Faculty of Mathematics and Informatics B-dul Eroilor 29, 500036, Brasov, Romania
Transilvania University of BrasovFaculty of Mathematics and InformaticsDepartment of Mathematics and InformaticsAssoc.Prof.Dr. Livia Sangeorzan

References

[1] Ahuja, R., Magnanti, T. and Orlin, J.(1993);

Network Flows. Theory, algorithms and applications, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1993.

[2] Bichot, C-E., Siarry, P. (2011), Graph Partitioning: Optimisation and Applications, ISTE Wiley.

[3] Hamacher, H.W. and Foulds, L.R. (1989); Algorithms for flows with parametric capacities, ZOR - Methods and Models of Operations Research, 33:21–37.

[4] Parpalea, M., Ciurea, E.(2013);

Partitioning Algorithm for the Parametric Maximum Flow, Applied Mathematics (Special Issue on Computer Mathematics), 4(10A):3–10.

[5] Parpalea, M.M. (2009);German Word Order, Bulletin of the Transilvania University of Brasov, Series IV, 2(51): 175–182.

[6] Parpalea, M. (2010); Min-Max algorithm for the parametric flow problem, Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics, 3(52):191– 198.

[7] Parvan, M., Ghionea, F., Flaut, C. (2008); A mathematical model of the relevant request determination in the transport problem, Mathematics and Computer in Business and Economics, Proc.of the 9th WSEAS Intl. Conf. on Mathematics and Computer in Business and Economics (MCBE'08), Bucureşti, 24-26 iunie 2008, 105–111.

[8] Ruhe, G. (1988); Complexity Results for Multicriterial and Parametric Network Flows Using a Pathological Graph of Zadeh, Zeitschrift fur Oper. Res., 32: 9–27.

[9] Ruhe, G. (1985); Characterization of all optimal solutions and parametric maximal flows in networks, Optimization, 16(1): 51–61.
http://dx.doi.org/10.1080/02331938508842988

[10] Sângeorzan, L., Parpalea, M., et al. (2010); Partitioning Preflow-pull Algorithm for the Parametric Net-work Flow Problem - a Linguistic Rule-based Constraints Optimisation Approach, Recent Advances in Neural Networks, Fuzzy Systems and Evolutionary Computing, Proc.of the 11th WSEAS International Conference on Neural Networks, Iasi, Romania, 111–116.

[11] Stumpff, A.M. (2013); The Law is a Fractal: The Attempt to Anticipate Everything, Loyola University Chicago Law Journal, 44.

[12] Yong, C., Chang-le, Lu (2006);

Using Multi-Thread Technology Realize Most Short-Path Parallel Algorithm, World Academy of Science, Engineering and Technology, 15: 11–13.

[13] High Court's Decision no 656/2012, given in a public hearing on February 9th, 2012, in the file no 1259/44/2010, http://www.iccj.ro/cautare.php?id=68146, accessed September 11th, 2014, at 13,40.
Published
2015-11-16
How to Cite
SANGEORZAN, Livia et al. A Preflow Approach to Maximum Flows in Parametric Networks Applied to Assessing the Legal Information. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 11, n. 1, p. 113-125, nov. 2015. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/1440>. Date accessed: 10 july 2020. doi: https://doi.org/10.15837/ijccc.2016.1.1440.

Keywords

Parametric preflow algorithm, partitioning technique, generative linguistics, legal information