Augmenting Path Algorithm for Routing Telephone Calls Problem

Title & Authors
Augmenting Path Algorithm for Routing Telephone Calls Problem
Lee, Sang-Un;

Abstract
This paper deals with the optimization problem that decides the routing of connection between multi-source and multi-sink. For this problem, there is only in used the mathematical approach as linear programming (LP) software package and has been unknown the polynomial time algorithm. In this paper we suggest the heuristic algorithm with $\small{O(mn)^2}$ time complexity to solve the optimal solution for this problem. This paper suggests the simple method that assigns the possible call flow quantity to augmenting path of ($\small{s_i,t_i}$) city pair satisfied with demand of ($\small{s_i,t_i}$). The proposed algorithm can be get the same optimal solution as LP for experimental data.
Keywords
Routing;Multiple-source;Multiple-sink;Multi-commodity flow;Flow network;Augmenting path;
Language
Korean
Cited by
References
1.
C. Gueret, X. Prins, and M. Sevaux, "Applications of Optimization with Xpress-MP: 12.3 Routing Telephone Calls," Dash Optimization Ltd., pp. 179-182, Feb. 2005.

2.
M. Edvall, "Publicity Campaign," Tomlab Optimization Inc, http://tomsym.com/examples/tomsym_routingcalls.html, Apr. 2009.

3.
M. Gondran and M. Minous, "Graphes et Algorithmes (2nd Ed.)," Eyrolles, 1990.

4.
R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, "Network Flows: Theory, Algorithms and Applications," Prentice Hall, Englewood Cliffs, NJ, 1993.

5.
T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, "Introduction to Algorithms (2nd ed.)," MIT Press and McGraw-Hill. pp. 788-789. 2001.

6.
S. Even, A. Itai, and A. Shamir, "On the Complexity of Timetable and Multi-commodity Flow Problems," SIAM Journal on Computing, Vol. 5, No. 4, pp. 691-703, 1976.

7.
C. Barnhart, C. A. Hane, E. L. Johnson, and G. Sigismondi, "A Column Generation and Partitioning Approach for Multi-commodity Flow Problems," Telecommunication Systems, Vol. 3, No. 3, pp. 239-258, Oct. 1995.

8.
G. Karakostas, "Faster Approximation Schemes for Fractional Multi-commodity Flow Problems," Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 166-173, 2002.

9.
K. Dudzinski, M. Libura, J. Majchrzak, and J. Sikorski, "Solution of Placement and Routing Problems in Telephone Exchange Unit Designs," Operations Research Spektrum, Vol. 10, No. 4, pp. 213-220, Dec. 1988.

10.
N. Gans and Y. P. Zhou, "A Call-Routing Problem with Service-Level Constraints," Journal of Operations Research, Vol. 51, No. 2, pp. 255-271, Mar. 2003.

11.
S. U. Lee, "An Optimization Rule for Channel Assignment Problem (CAP)," Journal of KSCI, Vol. 18, No. 6, pp. 37-45, Jun. 2013.

12.
S. U. Lee, "Minimum Network Connection Cost Algorithm for Partially Survivable Networks Problem of Cellular Telecommunication Systems," Journal of KSCI, Vol. 21, No. 1, pp. 59-64, Jan. 2016.

13.
S. U. Lee, "Independent Set Bin Packing Algorithm for Routing and Wavelength Assignment (RWA) Problem," Journal of KSCI, Vol. 20, No. 1, pp. 111-118, Jan. 2015.

14.
L. R. Ford and D. R. Fulkerson, "Maximal flow Through a Network," Canadian Journal of Mathematics, Vol. 8, No. 1, pp. 399-404, Jan. 1956.

15.
J. Edmonds, and R. M. Karp, "Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems," Journal of the ACM, Vol. 19, No. 2, pp. 248-264, Apr. 1972.

16.
Z. Uri, "The Smallest Networks on which the Ford-Fulkerson Maximum Flow Procedure may fail to Terminate," Theoretical Computer Science, Vol. 148, No. 1, pp. 165-170, Aug. 1995.

17.
D. Alevras and M. W. Padberg, "Linear Optimization and Extensions: Problems and Extensions," Universitext, Springer-Verlag, 2001.