Design of 2-level hierarchical ring networks

Hierarchical Ring Networks are widely used in communication systems, logistics and shared multiprocessors. It is hence imperative that efficient design of these structures has to be carried out, to reduce costs of their installation and help increase the ease of management. In this paper, we look at the problem of designing efficient 2-level Hierarchical Ring Networks, in the context of link costs optimization. 2-level HRNs only have two kinds of rings — local rings to connect disjoint sets of nodes and a global ring to interconnect all the local rings. We present an algorithm that is based on Simulated Annealing. We present results for scenarios containing upto 300 nodes. The results obtained from the algorithm are most encouraging.

[1]  Nicos Christofides.  Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

[2]  Donghan Kang,et al.  Design of local networks using USHRs , 2000, Telecommun. Syst..

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  Halit Üster,et al.  Algorithms for the design of network topologies with balanced disjoint rings , 2010, J. Heuristics.

[5]  Eli V. Olinick,et al.  SONET/SDH Ring Assignment with Capacity Constraints , 2003, Discret. Appl. Math..

[6]  Jiefeng Xu,et al.  Optimizing a Ring-Based Private Line Telecommunication Network Using Tabu Search , 1999 .

[7]  Stéphane Pérennes,et al.  All-to-all routing and coloring in weighted trees of rings , 1999, SPAA '99.

[8]  M. C. Sinclair,et al.  Design and dimensioning of dual-homing hierarchical multi-ring networks , 2000 .

[9]  S. Dreyfus,et al.  Thermodynamical Approach to the Traveling Salesman Problem : An Efficient Simulation Algorithm , 2004 .

[10]  Bernard Fortz,et al.  A tabu search algorithm for self-healing ring network design , 2003, Eur. J. Oper. Res..

[11]  Thomas R. Stidsen,et al.  Hierarchical Ring Network Design Using Branch-and-Price , 2005, Telecommun. Syst..

[12]  Michael Stumm,et al.  A performance comparison of hierarchical ring- and mesh-connected multiprocessor networks , 1997, Proceedings Third International Symposium on High-Performance Computer Architecture.

[13]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[14]  Hong Jiang,et al.  Hierarchical Ring Network Configuration and Performance Modeling , 2001, IEEE Trans. Computers.

[15]  R. H. J. M. Otten,et al.  The Annealing Algorithm , 1989 .

[16]  Kemal Altinkemer,et al.  Topological design of ring networks , 1994, Comput. Oper. Res..

[17]  John P. Fonseka,et al.  Hierarchical self-healing rings , 1995, TNET.

[18]  Yi Zhou,et al.  A 2-approximation algorithm for path coloring on a restricted class of trees of rings , 2003, J. Algorithms.

[19]  Anil Kumar. Gupta.  On a generalized travelling salesman problem. , 1986 .