Skip to main content
SpringerLink
Log in

A new approach for solving the network problems

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

This study aims to optimize the number of nodes and arcs in a constructed network employing a given criteria. For this, we subject the constructed network using the methods like Shortest Path (SP), Critical Path (CP) and Max-Flow (MF) between any pair of nodes. A set of iterative algorithms have been generated using matrix operations to meet the above requirement, which is named as Pandit’s algorithm. The equivalent algorithms for SP, CP and MF are hereby represented as Pandit’s Mini-additive, Maxi-additive and Max-min algorithms respectively. The generated algorithms take less number of iterations when compared to the established methods. The proposed new algorithms are shown with suitable numerical examples and discuss their merits over the established methods. These new algorithms take less computational time and hence suggested for solving the bulk networks such as transportation GIS, telecommunication networks, information systems, project scheduling etc.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Adelson-velsky, G.M., Levner, E.: Routing information flows in network. A Generalisation of Dijkstra’s Algorithm. Proc. Internat. Conf. “Distributed Communication Networks: Theory and applications”- 1999, Tel Aviv University, pp. 1–4 (1999a)

  2. Ahuja, R.K., Magnanti, T. L., Orlin, J.B.: Network Flows. Theory, Algorithms and Applications. Prentice Hall, Englewood Cliffs, N. J (1993)

  3. Bartusch, M., Mhring, R.H., Radermacher, F.J.: Scheduling Project Networks with Resource Constraints and Time Windows. Ann. Oper. Res. 5(4), 321–344 (1989)

    Google Scholar 

  4. Brucker, P., Drexl, A., Mohring, R., Neumann, K., Pesch, E.: Resource constrained Project scheduling: Notation, Classification, Models and Methods. EJOR 112, 3–41 (1999)

    Article  Google Scholar 

  5. Chabini, I.: Discrete dynamic shortest path problems in transportation applications, Transportation Research Record 1645 (1998)

  6. Chen, A., Kim, J., Zhou, Z., Chootinan, P.: An alpha reliable network design problems. Transportation Research Record 2029(−1), pp 49–57 (2007)

  7. Cormen, T.H., Leiserson, C.E., Revest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)

    Google Scholar 

  8. Crowston, W.: Decision CPM: Network reduction and solution. Oper. Res. Quart. 21(40), 435–445 (1970)

    Article  Google Scholar 

  9. De Mello, L.S.H., Sanderson, A.C.: AND/OR graph representation of assembly plans. IEEE Trans. Robotics Automat 6(2), 188–199 (1990)

    Article  Google Scholar 

  10. De Reyck, B., Demeulemeester, E., and Herroelen, W.: Algorithms for Scheduling Projects with Generalised Precedence Relations. In Project Scheduling—Recent Models, Algorithms and Applications, J. weglarz, ed. Kluwer Academic Publ., Boston, 77–105 (1999)

  11. Dijkstra, E.W.: A note on two problems in Connection with graphs. Numer. Math. 1, 269–271 (1959)

    Article  Google Scholar 

  12. Dinic, E.A.: Algorithm for solution of a problem of maximum flow in networks with power estimation. Soviet Mayh. Dokl. 11, 1277–1280 (1970)

    Google Scholar 

  13. Dinic, E.A.: The fastest algorithm for the PERT problems with AND- and OR- nodes. Proc. Workshop on Combinatorial Optimization. Waterloo, Ontario, Canada. University of Waterloo press, Waterloo, Ontario (1990)

  14. Edmonds, J., Karp, R.M.: Theoretical improvement in algorithmic efficiency for network flow problems. J. Assoc. Comput. Mach. 19, 248–264 (1972)

    Article  Google Scholar 

  15. Elmaghraby, S.E., Kamburowski, J.: The analysis of activity networks under generalized precedence relations. Manag. Sci. 38(9), 1245–1263 (1992)

    Article  Google Scholar 

  16. Fest, A., Mohring, R.H., Stork, F., and Uetz, M.: Resource constrained project scheduling with time windows: A branching scheme based on dynamic release dates. Tech. Rep. 596, TU Berlin (1999)

  17. Gabow, H.N., Goemans, M.X., Williamson, D.P.: An efficient approximation algorithm for the survivable network design problem. Math. Program. 82(1), 13–40 (1998)

    Article  Google Scholar 

  18. Gavish, B.: Topological design of telecommunication network –Local access design methods. Ann. Oper. Res. 33, 17–71 (1991)

    Article  Google Scholar 

  19. Gen, M., Kumar, A., Kim, J.R.: Recent network design techniques using evolutionary algorithms. Int. J. Prod. Econ. 98(2), 251–261 (2005)

    Article  Google Scholar 

  20. Gillies, D., Liu, J.: Scheduling tasks with AND/OR precedence constraints. SIAM J. Comp 24(4), 787–810 (1995)

    Article  Google Scholar 

  21. Greig, D., et al.: Exact maximum a posteriori estimation for binary images. Journal of the Royal Statistical Society, Series B 51(2), 271–279 (1989)

    Google Scholar 

  22. Herroelen, W., Demeulemeester, E., De Reyck, B.: A Classification Scheme for Project Scheduling Problems. Kluwer Academic Publishers, Chapter, Handbook on Recent Advances in Project Scheduling (1999). 3

    Google Scholar 

  23. Jacob, R., Marathe, M.V., and Nagel, K.: A computational study of routing algorithms for realistic transportation networks, 2nd Workshop on Algorithmic Engineering (WAE’98), Saarbrücken, Germanz, August 19–21 1998, received via personal communication (1998)

  24. Karzanov, A.V.: Determining the maximal flow in a network by the method of preflows. Inform. Process. Lett. 38, 434–437 (1991)

    Google Scholar 

  25. Klein, P., Rao, S., Rauch, M., and Subramaniyan, S.: Faster shortest path algorithms for planar graphs. In: Proceedings of 26th ACM Symposium on Theory of Computing, 27–37 (1994)

  26. Kumar, S., and Gupta, P.: An incremental algorithm for maximum flow problem. Vol. 2(1), pp 1–16 (2003)

  27. Lawler, E.L.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New Yaok (1976)

    Google Scholar 

  28. Ford Jr., L.R., Fulkerson, D.R.: Maximal flow through a network. Canad. J. Math 8, 399–404 (1956)

    Article  Google Scholar 

  29. Neumann, K., Schwindt, C.: Activity-on-node networks with minimal and maximal time lags and their application to make-to-order production. OR Spectr. 19, 205–217 (1997)

    Google Scholar 

  30. Pannerselvam, R.: Operations Research second edition. Prentice Hall of India private limited, New Delhi (2006)

    Google Scholar 

  31. Pandit, S.N.N.: Shortest paths without Loops and the TSP (Privately circulated) (1964)

  32. Pandit, S.N.N.: Some observations on the Longest Path Problems. Opns. Res 12(2), 361–364 (1964)

    Article  Google Scholar 

  33. Schwindt, C.: A branch bound algorithm for the resource- constrained scheduling problems with minimal and maximal time lags. Tech. Rep. WIOR −489, Univ. Karlsruche (1998)

  34. Shulman, A., Vachani, R.: A decomposition algorithm for capacity expansion of local access networks. IEEE Trans. Commun. 41(7), 1063–1074 (1993)

    Article  Google Scholar 

  35. Sridhar, V., Park, J.S.: Benders-and-cut algorithms for fixed-charge capacitated network design problems. Eur. J. Oper. Res. 125, 622–632 (2000)

    Article  Google Scholar 

  36. Volkar Kaibal, Matthias A.F Peinhardt.: On the bottleneck shortest path problems. ZIB Report 06–22, May (2006)

  37. Gupta, J.N.D.: TSP—A survey of theoretical developments and applications. Opsearch 5(4), 181–192 (1967)

    Google Scholar 

  38. Ramana, V.V.V.: A class of combinatorial programming problems—using Lexi-search approach, Ph.D. Thesis, S.K.D. University, P.G. Centre, Kurnool, A.P., India (1995)

  39. Subramanyam, Y.: Scheduling Transportation and Allied Combinatorial programming problems. Ph.D., Thesis, REC, Kakatiya University, Warangal (1980)

    Google Scholar 

  40. Murthy, S.: Combinatorial programming—a pattern recognition approach. PhD, Thesis REC, Warangal, India (1979)

    Google Scholar 

Download references

Acknowledgment

The first author expresses my deep sense of reverence and gratitude to the research supervisor Prof. M. Sundara Murthy, Department of Mathematics, Sri Venkateswara University, Tirupati for suggesting this problem for investigation. It is solely due to his immense interest, competence and exceptional guidance, critical analysis, transcendent and concrete suggestions enlightened discussions, which cumulatively are responsible for the successful execution of this work.

Author information

Authors and Affiliations

  1. Department of Mathematics, Sri Venkateswara University, Tirupati, Andhra Pradesh, 517502, India

    Purusotham Singamsetty & M. Sundara Murthy

Authors
  1. Purusotham Singamsetty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Sundara Murthy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Purusotham Singamsetty.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Singamsetty, P., Murthy, M.S. A new approach for solving the network problems. OPSEARCH 49, 1–21 (2012). https://doi.org/10.1007/s12597-012-0063-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-012-0063-8

Keywords

Search

Navigation