TY - GEN

T1 - Improved bounds for all optical routing

AU - Aumann, Yonatan

AU - Rabani, Yuval

PY - 1995/1/22

Y1 - 1995/1/22

N2 - We consider the problem of routing in networks employing all optical routing technology. In these networks, messages travel in optical form and switching is performed directly on the optical signal. By using different wavelengths, several messages may use the same edge concurrently, However, messages assigned the same wavelength must use disjoint paths, or else be routed at separate rounds. No buffering at intermediate nodes is available. Thus, routing in this setting entails assigning wavelengths, paths, and time slots for the different messages. For arbitrary bounded degree networks, we show that any permutation can be routed efficiently in one round using at most O(log2n/β2) wavelengths, where β is the edge expansion of the network. This improves a quadratic factor on previous results, and almost matches the ω(l/β2) existential lower bound. We consider two of the more popular architectures for parallel computers. For bounded dimension arrays we give the first per-instance approximation algorithm. Given a limited number of wavelengths and a set of messages to be routed, the algorithm approximates to within polylogarithmic factors the optimal number of rounds necessary to route all messages. Previous results for arrays give only worst-case performance. Finally, we show that on the hypercube any permutation can be routed using only a constant number of wavelengths. The previous known bound was O(logre).

AB - We consider the problem of routing in networks employing all optical routing technology. In these networks, messages travel in optical form and switching is performed directly on the optical signal. By using different wavelengths, several messages may use the same edge concurrently, However, messages assigned the same wavelength must use disjoint paths, or else be routed at separate rounds. No buffering at intermediate nodes is available. Thus, routing in this setting entails assigning wavelengths, paths, and time slots for the different messages. For arbitrary bounded degree networks, we show that any permutation can be routed efficiently in one round using at most O(log2n/β2) wavelengths, where β is the edge expansion of the network. This improves a quadratic factor on previous results, and almost matches the ω(l/β2) existential lower bound. We consider two of the more popular architectures for parallel computers. For bounded dimension arrays we give the first per-instance approximation algorithm. Given a limited number of wavelengths and a set of messages to be routed, the algorithm approximates to within polylogarithmic factors the optimal number of rounds necessary to route all messages. Previous results for arrays give only worst-case performance. Finally, we show that on the hypercube any permutation can be routed using only a constant number of wavelengths. The previous known bound was O(logre).

UR - http://www.scopus.com/inward/record.url?scp=85000332498&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85000332498

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 567

EP - 576

BT - Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

PB - Association for Computing Machinery

T2 - 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

Y2 - 22 January 1995 through 24 January 1995

ER -