Abstract
The Minimum Cost Network Flow Problem (MCNFP) constitutes perhaps the most important of the research area of Network Optimization. Recently a new category of algorithms for the MCNFP have been developed. These algorithms belong to a special “exterior type” simplex category and they feature significant tree modifications. This paper presents a new didactic tool for the teaching of this type of algorithms. The proposed educational software can be used in courses like “Graph Theory” or “Combinatorial Optimization”. This tool has been implemented using the Java Programming language and it is platform independed. It constitutes a friendly application, for the instructor, as also for the novice student. Furthermore, its use is analytically shown through an illustrative example. Benefits and drawbacks are thoroughly described in order to support the significance of this visualization tool in computer-aided education and also possible future work is discussed.
Similar content being viewed by others
References
Ahuja, R. K., Magnanti, T. L., Orlin, J. B. and Reddy, M. R. (1995), “Applications of Network Optimization”, in: M.O. Ball, T.L. Magnanti, C.L. Monma and G.L. Nemhauser (Eds),Handbooks of Operations Research and Management Science, Network Models, Elsevier Publications, 7, 1–83.
Almstrum, V.L., Hazzan, O., Guzdial, M. and Petre, M. (2005), “Challenges to computer science education research”,in Proc. of the 36 th SIGCSE Technical Symposium on Computer Science Education, St. Louis, Missouri, USA.
Andreou, D., Paparrizos, K., Samaras, N. and Sifaleras, A. (2005), “Application of a New Network-enabled Solver for the Assignment Problem in Computer-aided Education”,Journal of Computer Science, Science Publications, New York, USA, 1(1), 19–23.
Bazaraa, M.S., Jarvis, J.J. and Sherali, H.D. (2005),Linear Programming and Network Flows, 3rd ed., Wiley Publications.
Byrne, M.D., Catrambone, R. and Stasko, J.T. (1999), “Evaluating animations as student’s aids in learning computer algorithms”,Computers and Education, 33(4), 253–278.
Cordova, J.L. (2003), “The use of web-based visualization techniques and its effect on student comprehension”,Journal of Computing Sciences in Colleges, 18(6), 67–71.
Dosios, K., Paparrizos, K., Samaras, N. and Sifaleras, A. (2003), “NetPro, an E=ducational Platform for Network Optimization”,in Proc. of the 16 th National Conference of Hellenic Operational Research Society, Larisa, Greece, 1, 287–295.
Geranis, G., Paparrizos, K. and Sifaleras, A. (2008), “A dual exterior point simplex type algorithm for the minimum cost network flow problem”, accepted for publication in theYugoslav Journal of Operations Research.
Glover, F., Klingman, D. and Phillips, N. (1992),Network Models in Optimization and Their Applications in Practice, 1st ed., Wiley Publications.
Hendrix, T.D., Cross, J.H. and Barowski, L.A. (2004), “An extensible framework for providing dynamic data structure visualizations in a lightweight IDE”,in Proc. of the 35 th SIGCSE Technical Symposium on Computer Science Education, ACM Press, Norfolk, Virginia, USA.
Hundhausen, D.C., Douglas, A.S. and Stasko, T.J. (2002), “A meta-study of algorithm visualization effectiveness”, Journal of Visual Languages and Computing, 13(3), 259–290.
Karagiannis, P., Markelis, I., Paparrizos, K., Samaras, N. and Sifaleras, A. (2006), “E — learning technologies: employing matlab web server to facilitate the education of mathematical programming”,International Journal of Mathematical Education in Science and Technology, Taylor & Francis Publications, 37(7), 765–782.
Kehoe, C., Stasko, J.T. and Taylor, A. (2001), “Rethinking the evaluation of algorithm animations as learning aids: an observational study”,International Journal of Human-Computer Studies, 54(2), 265–284.
Lawrence, A.W., Badre, A.N. and Stasko, J.T. (1994), “Empirically evaluating the use of animations to teach algorithms”,in Proc. of the IEEE Symposium on Visual Languages, U.S.A.
Lazaridis, V., Paparrizos, K., Samaras, N. and Sifaleras, A. (2007), “Visual LinProg: A Web-based Educational Software for Linear Programming”,Computer Applications in Engineering Education, Wiley Periodicals Inc., 15(1), 1–14.
Lazaridis, V., Samaras, N., Zissopoulos, D. (2003), “Visualization and teaching simplex algorithm,in Proc. of the 3 rd IEEE International Conference on Advanced Learning Technologies, 9–11 July, Athens, Greece, 270–271.
Luengo, V. (2005), “Some didactical and Epistemological Considerations in the Design of Educational Software: The Cabri-euclide Example”,International Journal of Computers for Mathematical Learning, 10(1), 1–29.
Naps, T. (1996), “Algorithm Visualization Delivered Off the World Wide Web - Why and How”,in Proc. of the Association for Computing Machinery’s SIGCSE/SIGCUE Conference on Integrating Technology into Computer Science Education, Barcelona, Spain.
Naps, T. (1997), “Algorithm visualization on the World Wide Web - the difference Java makes!,in Proc. of the 2 nd Conference on Integrating technology Into Computer Science Education, Uppsala, Sweden.
Papamanthou, C., Paparrizos, K., and Samaras, N. (2005), “A Parametric Visualization Software for the Assignment Problem”,Yugoslav Journal of Operations Research, 15(1), 1–12.
Paparrizos, K., Samaras, N. and Sifaleras, A. (2004), “A learning tool for the visualization of general, directed or undirected rooted trees”, in: K. Morgan & J.M. Spector (eds),WIT Transactions on Information and Communication Technologies, 30, WIT Press, 205–213,presented at the 1 st International Conference on New Learning Paradigms and New Learning Tools, 10–12 May, Skiathos, Greece.
Paparrizos, K., Samaras, N. and Sifaleras, A. (2008), “An exterior Simplex type algorithm for the minimum cost network flow problem”,accepted for publication in Computers & Operations Research, Elsevier Ltd.
Saraiya, P., Shaffer, C.A., McCrickard, D.S. and North, C. (2004), “Effective features of algorithm visualizations”,in Proc. of the 35 th SIGCSE Technical Symposium on Computer Science Education, ACM Press, Norfolk, Virginia, USA.
Sinclair, N., Zazkis, R. and Liljedahl, P. (2004), “Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts”,International Journal of Computers for Mathematical Learning, 8(3), 235–263.
Smith, G.G. and Ferguson, D. (2004), “Diagrams and math notation in e-learning: growing pains of a new generation”,International Journal of Mathematical Education in Sciences and Technology, 35(5), 681–695.
Varkas, G., Kostoglou, V. and Paparrizos, K. (2005), “Broadband Networks and Services: Innovative Means of Human Communication”,in Proc. of the 4 th International Conference on New Horizons in Industry and Education, Corfu, Greece, 52–57.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Andreou, D., Paparrizos, K., Samaras, N. et al. Visualization software of the network exterior primal simplex algorithm for the minimum cost network flow problem. Oper Res Int J 7, 449–463 (2007). https://doi.org/10.1007/BF03024857
Issue Date:
DOI: https://doi.org/10.1007/BF03024857