Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Packing cycles in undirected graphs
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Pattern matching with address errors: rearrangement distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
A 10/7 + ε approximation for minimizing the number of ADMs in SONET rings
IEEE/ACM Transactions on Networking (TON)
Better bounds for minimizing SONET ADMs
Journal of Computer and System Sciences
Hardness and approximation of traffic grooming
Theoretical Computer Science
On the cost of interchange rearrangement in strings
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Approximability of packing disjoint cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Traffic grooming in path, star, and tree networks: complexity, bounds, and algorithms
IEEE Journal on Selected Areas in Communications - Part Supplement
Traffic grooming in WDM networks: past and future
IEEE Network: The Magazine of Global Internetworking
Hi-index | 5.23 |
We study traffic grooming in optical network design, where the goal is to aggregate low-bandwidth traffic streams to utilize efficiently high-bandwidth media such as wavelength channels. More precisely, given traffic demands to be routed in a network, the design problem is to define a collection of light paths such that each demand can follow a sequence of consecutive light paths. Each light path has a unit-wavelength bandwidth, and multiple sub-wavelength demands may share a common light path. Traffic must enter and depart from a light path at its two endpoints only. Most previous work on grooming focused on the ring topology and typically involved only uniform bandwidth demands, whereas we deal with more general settings. Two objectives are considered. One is to minimize the total cost of equipment necessary to support the light paths; the other is simply to minimize the number of light paths. Even for the extremely restricted special case of a line topology and traffic demands that request half wavelength bandwidth, we show that both objectives are APX-hard to optimize, which means we cannot approximate the optimum arbitrarily closely. On the other extreme of generality, for arbitrary network topologies and traffic demands that request arbitrary amounts of bandwidth, we show a logarithmic approximation for cost minimization and a 2-approximation for minimizing light path counts. Furthermore, we discover that the special case of half-wavelength demands has rich combinatorial properties, closely related to graph problems such as cycle packing and pattern matching problems such as interchange distance in strings. We show how to approximate both objectives up to small constant factors in this case, while similarly improving the approximation and hardness of the interchange distance problem as well.