Topological design of ring networks

doi:10.1016/0305-0548(94)90029-9

Computers & Operations Research

Volume 21, Issue 4, April 1994, Pages 421-431

https://doi.org/10.1016/0305-0548(94)90029-9 Get rights and content

Abstract

In this paper the shortcomings of conventional ring networks are discussed and how these shortcominings are solved by the enhanced ring architecture is explained. Enhanced ring architecture is a two level ring network connecting the local rings by a backbone ring. Studied is the ring network design problem—the formation of local loops with a size restriction connected to a backbone ring. The Parallel Savings Algorithm which generates good feasible solutions is presented. The K Iterated Travelling Salesman Tours Partitioning is studied and analyzed for its worst case error. This algorithm is based on partitioning a multi-center travelling salesman tour in order to generate a feasible solution to the ring network design problem. It has a worst case error bound of $4 − 32 K$ where K is the size of the local rings when K⩾3. The heuristic solution cost is at most $4 − 32 K$ times the optimum value. It is based on the Christofides' extended heuristic for the multi-center travelling salesman problem which makes the procedure a polynomial one.

References (23)

B.K. Penney et al.
Survey of computer communications loop networks: Part 1
Comp. Commun.
(1979)
K. Altinkemer et al.
Heuristics for unequal weight delivery problems with a fixed error guarantee
Ops res. Lett.
(1987)
W. Stalings
Local networks.
Comput. Surv.
(1984)
W. Stallings
Local Networks, An Introduction
(1987)
B. Gavish
Design issues in large networks of personnel computers. Working paper
(1988)
L. Bodin et al.
Routing and scheduling of vehicles and crews the state of the art
Computer ops. Res.
(1983)
N. Christofides et al.
An algorithm for the vehicle dispatching problem
Ops res. Q
(1969)
N. Christofides et al.
The Vehicle Routing Problem ‘Combinatorial Optimization’
(1979)
N. Christofides et al.
Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations
Math. Program.
(1981)
M.L. Fisher et al.
A generalized assignment heuristic for vehicle routing
Networks
(1981)

G. Frederickson et al.

Approximation algorithms for some routing problems

SIAM J. Comput.

(1978)

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^†: K. Altinkemer is Associate Professor of Management at the Krannert School of Management, Purdue University. He has the B.S. in Industrial Engineering, Bogazici, and M.S. and Ph.D. in Computers and Information Systems. Professor Altinkemer's primary teaching interests are computer communication networks, database management systems, management information systems, and economics of information systems. His current research interests include design of local access computer networks and backbone networks, combined iterative network design procedures and design and analysis of local area networks. His other topics or areas of expertise include distributed systems, applied operations research, database management systems, and applications of neural networks to network design. His publications have appeared in Operations Research, Management Science, Operations Research Letters, ORSA Journal on Computing and Transportation Science. Prior to joining the Krannert faculty, he was an instructor at the University of Rochester.

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Topological design of ring networks

Abstract

Comp. Commun.

Ops res. Lett.

Local networks.

Comput. Surv.

Local Networks, An Introduction

Design issues in large networks of personnel computers. Working paper

Routing and scheduling of vehicles and crews the state of the art

Computer ops. Res.

An algorithm for the vehicle dispatching problem

Ops res. Q

The Vehicle Routing Problem ‘Combinatorial Optimization’

Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations

Math. Program.

A generalized assignment heuristic for vehicle routing

Networks

Approximation algorithms for some routing problems

SIAM J. Comput.