Routing Algorithms for Ring Networks

In this thesis, we study routing problems on ring networks. The ring is a popular topology for communication networks and has attracted much research attention. A communication application on a ring network can be regarded as a set of connection requests, each of which is represented by a set of nodes to be connected in the ring network. To implement a communication application, we need to develop a routing algorithm to find a path connecting all the nodes involved in each connection request. One of the most important optimization problems for the communication on ring networks is to develop a routing algorithm such that the maximum congestion (i.e., the maximum number of paths that use any single link in the ring) is minimized. This problem can be formulated as the Minimum Congestion Hypergraph Embedding in a Cycle (MCHEC) problem with a set of connection requests represented by a hypergraph. A special case of the MCHEC problem, in which each connection request involves exactly two nodes, is known as the Minimum Congestion Graph Embedding in a Cycle problem. A more general case, in which connection requests may have non-uniform bandwidth requirements, is known as the Minimum Congestion Weighted Hypergraph Embedding in a Cycle problem. The Minimum Congestion Graph Embedding in a Cycle problem is solvable in polynomial time, and the other problems are NP-hard. In this thesis, we focus on the MCHEC problem and propose efficient algorithms in three categories. In the first category is a 1.8-approximation algorithm that improves the previous 2-approximation algorithms. In the second category is an algorithm that computes optimal solutions for the MCHEC problem. This algorithm runs in polynomial time for subproblems with constant maximum congestions, and is more efficient in terms of the time complexity than the previous algorithm that solves the same problem. The third category contains two heuristic approaches. According to our simulation results, both heuristics have lower time complexities and better practical performance than a well known heuristic.