Parallel algorithm for the routing problem: an implementation in the parallel computer IBM-SP2

In this article is presented and implemented a parallel method for solving the routing problem in packet-switched communication networks. This problem can be formulated as a multicommodity flow problem using a convex criterion. The algorithm presented here solves iteratively the multiflow problem, breaking it up in the most possible independent form such as subproblems of single flow commodities The independence between the calculations enables a simultaneous solution of the subproblems and the parallel implementation. The results of the parallel algorithm were used to establish a comparison with the sequencial algorithm and to perform a speedup analysis. The parallel library used was the PVM.

[1]  Paul Tseng,et al.  Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems , 1988, Oper. Res..

[2]  Mario Gerla,et al.  Optimal Routing in a Packet-Switched Computer Network , 1974, IEEE Transactions on Computers.

[3]  D. Bertsekas,et al.  Projected Newton methods and optimization of multicommodity flows , 1982, CDC 1982.

[4]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[5]  Ronald D. Armstrong,et al.  A new strongly polynomial dual network simplex algorithm , 1997, Math. Program..

[6]  Leonard Kleinrock,et al.  Communication Nets: Stochastic Message Flow and Delay , 1964 .

[7]  Hanif D. Sherali,et al.  Linear Programming and Network Flows , 1977 .

[8]  Éva Tardos,et al.  Polynomial dual network simplex algorithms , 2011, Math. Program..

[9]  Tomasz Radzik.  Fast deterministic approximation for the multicommodity flow problem , 1995, SODA '95.

[10]  Alexander V. Karzanov,et al.  Multiflows and disjoint paths of minimum total cost , 1997, Math. Program..

[11]  John K. Antonio,et al.  Distributed iterative aggregation algorithms for box-constrained minimization problems and optimal routing in data networks , 1989 .

[12]  Ravindra K. Ahuja,et al.  A new pivot selection rule for the network simplex algorithm , 1997, Math. Program..

[13]  M. Schwartz,et al.  The Gradient Projection Algorithm for Multiple Routing in Message-Switched Networks , 1976, IEEE Trans. Commun..

[14]  Michel Minoux,et al.  Graphs and Algorithms , 1984 .

[15]  J. Castro,et al.  An implementation of linear and nonlinear multicommodity network flows , 1996 .

[16]  D. Bertsekas,et al.  Distributed asynchronous optimal routing in data networks , 1984, The 23rd IEEE Conference on Decision and Control.

[17]  Jack Dongarra,et al.  Pvm 3 user's guide and reference manual , 1993 .

[18]  Robert E. Tarjan,et al.  Dynamic trees as search trees via euler tours, applied to the network simplex algorithm , 1997, Math. Program..

[19]  T. Stern,et al.  A Class of Decentralized Routing Algorithms Using Relaxation , 1977, IEEE Trans. Commun..

[20]  Richard D. McBride,et al.  Progress Made in Solving the Multicommodity Flow Problem , 1998, SIAM J. Optim..

[21]  R. V. Helgason,et al.  Algorithms for network programming , 1980 .

[22]  Robert G. Gallager,et al.  A Minimum Delay Routing Algorithm Using Distributed Computation , 1977, IEEE Trans. Commun..

[23]  D. Bertsekas,et al.  Partially asynchronous, parallel algorithms for network flow and other problems , 1990 .