Efficient Algorithms for Computing Shortest Path on Directed and Undirected Double-Loop Networks

by Chen, Ming-You

In this thesis, we present two e cent algorithms to compute shortest path between pair of vertices in directed and undirected double-loop networks. The algorithm for undirected double-loop networks is based on the concept "packed basis" proposed by Janez Zerrovnik and Toma z Pisanski. With O(logN) preprocessing time, both algorithms need only constant time to compute the shortest path between any pair of vertices in the network. This is an improvement of the best known algorithm, which needs O(l) time, where l is the length of the path in the directed double-loop networks. These algo- rithms are useful in message routing in the double-loop networks. Once the network has been constructed, the parameters for computing the shortest paths can be computed. At the time a message is to be delivered, the algo- rithm needs only constant time to determine which edge the message should be sent.