Efficient routing in optical networks
Journal of the ACM (JACM)
All-to-all routing and coloring in weighted trees of rings
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Ring routing and wavelength translation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Efficient collective communication in optical networks
Theoretical Computer Science
SIAM Review
The complexity of path coloring and call scheduling
Theoretical Computer Science
Routing permutations and 2---1 routing requests in the hypercube
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
An Efficient Algorithm for the Ring Loading Problem with Integer Demand Splitting
SIAM Journal on Discrete Mathematics
Approximation algorithms for routing and call scheduling in all-optical chains and rings
Theoretical Computer Science
Wavelength assignment and generalized interval graph coloring
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Routing of Permutations on Rings
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
The permutation-path coloring problem on trees
Theoretical Computer Science - Latin American theoretical informatics
Permutation routing in double-loop networks: design and empirical evaluation
Journal of Systems Architecture: the EUROMICRO Journal
Demand Routing and Slotting on Ring Networks
Demand Routing and Slotting on Ring Networks
Hi-index | 0.00 |
Given a network G and a demand D of communication requests on G, a routing for (G,D) is a set of directed paths of G, each from the source to the destination of one request of D. The Routing and Wavelength Assignment Problem seeks a routing R for (G,D) and an assignment of wavelengths to the directed paths in R such that the number of wavelengths used is minimized, subject to that any two directed paths with at least one common arc receive distinct wavelengths. In the case where G is a ring, this problem is known as the Ring Routing and Wavelength Assignment Problem (RRWA). If in addition D is symmetric (that is, (s,t)@?D implies (t,s)@?D) and the directed paths for requests (s,t) and (t,s) are required to be reverse of each other, then the problem is called the Symmetric Ring Routing and Wavelength Assignment Problem (SRRWA). A demand is called a permutation demand if, for each vertex v of G, the number of requests with source v and the number of requests with destination v are the same and are equal to 0 or 1. A symmetric permutation demand is called an involution demand. In this paper we prove that both RRWA and SRRWA are NP-complete even when restricted to involution demands. As a consequence RRWA is NP-complete when restricted to permutation demands. For general demands we prove that RRWA and SRRWA can be solved in polynomial time when the number of wavelengths is fixed. Finally, we answer in the negative an open problem posed by Gargano and Vaccaro and construct infinitely many counterexamples using involution demands.