Liwu Liu

Wavelength assignment in WDM rings to minimize SONET ADMs

We study wavelength assignment for lightpaths over WDM rings to minimize the SONET ADMs (add/drop multiplexers) used. This problem has attracted much attention recently. However, its computational complexity remains unknown, and the only known heuristic (Gerstel et al., 1998) which does not allow the splitting of lightpaths is problematic in terms of both the algorithm itself and its performance analysis. We first prove the NP-completeness of this problem, followed by a nontrivial randomized (3+e)/(1+e)-approximation scheme. We then present a tighter lower bound on the minimum number of ADMs required. After that, we show the incorrectness of the known heuristic and then modify it to make it correct. We also propose three additional heuristics. Their performances are compared through extensive simulation studies.

Grooming of arbitrary traffic in SONET/WDM rings

SONET add-drop multiplexers (ADMs) are the dominant cost in SONET/WDM rings. They can potentially be reduced by optical bypass via wavelength add-drop multiplexers (WADMs) and traffic grooming. While many works have been done on the grooming of all-to-all uniform traffic and one-to-all traffic, the grooming of arbitrary traffic have not been studied yet. We first prove the NP-hardness of this problem. We then presents two general lower bounds on the minimum ADM cost. After that we propose a two-phased algorithm. The two subproblems in these two phases are both NP-hard. Various approximation algorithms are proposed to each subproblem, and their performances are discussed.

Optimal placement of wavelength converters in trees and trees of rings

In wavelength-routed optical networks, wavelength converters can potentially reduce the requirement on the number of wavelengths. The problem of placing a minimum number of wavelength converters in a WDM network so that any routing can be satisfied using no more wavelengths than if there were wavelength converters at every node was raised in Wilfong et al. (1998) and shown to be NP-complete in general WDM networks. Recently, it was proved in Kleinberg et al. (1999) that this problem is as hard as the well-known minimum vertex cover problem. In this paper, we further their study in two topologies that are of more practical concrete relevance to the telecommunications industry: trees and tree of rings. We show that the optimal wavelength converter placement problem in these two practical topologies are tractable. Efficient polynomial-time algorithms are presented.

Energy-Efficient Spectrum Sensing for Cognitive Radio Enabled Remote State Estimation Over Wireless Channels

The performance of remote estimation over wireless channels is strongly affected by sensor data losses due to interference. Although the impact of interference can be alleviated by applying cognitive radio technique which features in spectrum sensing and transmitting data only on clear channels, the introduction of spectrum sensing incurs extra energy expenditure. In this paper, we investigate the problem of energy-efficient spectrum sensing for remotely estimating the state of a general linear dynamic system, and formulate an optimization problem which minimizes the total sensor energy consumption while guaranteeing a desired level of estimation performance. We model the problem as a mixed integer nonlinear program and propose a simulated annealing based optimization algorithm which jointly addresses when to perform sensing, which channels to sense, in what order and how long to scan each channel. Simulation results demonstrate that the proposed algorithm well balances the sensing energy and transmission energy expenditure and can achieve the desired estimation performance.

Select line speeds for single-hub SONET/WDM ring networks

Minimizing SONET ADM costs in single-hub SONET/WDM ring networks via traffic grooming has been discussed in a number of previous works. Previous work gives the exact minimum costs of uniform traffic in both unidirectional path-switched ring (UPSR) and two-fiber bidirectional line-switched ring (BLSR/2) and proves that the BLSR/2 would never be more expensive than UPSR under any traffic pattern, if all wavelengths have the same capacity. We consider how to groom both uniform and non-uniform traffic to minimize the cost of ADMs in the single-hub UPSR and BLSR/2 with mixed line speeds. We especially explore the grooming of traffic when wavelengths have two different capacities g/sub 1/=1 and g/sub 2/=4. We show that the problem can be confined to just consider the traffic request r/sub i//spl les/4 for all non-hub nodes i. By adopting the same cost model of Gerstel, Lin and Sasaki (see Proc. IEEE Infocom 99), i.e., ADMs with speed g/sub 1/=1 and g/sub 2/=4 cost 1 and 2.5 respectively, we provide optimal traffic partition and grooming for uniform traffic demands, and develop optimal or suboptimal solutions for non-uniform traffic demands, depending on the range of all demands from non-hub nodes.

Optimal placement of wavelength converters in trees, tree-connected rings, and tree of rings

In wavelength routed optical networks, wavelength converters can potentially reduce the requirement on the number of wavelengths. A recent study [Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms (1998)] raised the following problem: choose a minimum number of nodes in a WDM network to place wavelength converters so that any set of paths requires the same number of wavelengths as if wavelength converters were placed at all node. This problem is referred to as minimum sufficient set problem. It was shown to be NP-complete in general WDM networks [Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms (1998)], and be as hard as the well-known minimum vertex cover problem [Proceedings of 10th ACM-SIAM Symposium on Discrete Algorithms (1999)]. In this paper, we extend their study in trees, tree-connected rings, and tree of rings which are widely used topologies in the telecommunications industry. We show that the optimal wavelength converter placement problem in these two practical topologies are tractable. Efficient polynomial-time algorithms are presented.

Wavelength assignment to minimize requirement on tunable range of optical transceivers in WDM networks

In this paper we consider WDM networks with a tunable transmitter and a fixed-wavelength receiver at each station (similar results hold when the transmitter is fixed and the receiver is tunable). Traditionally, each station is required to be able to access all wavelength channels used in the network. Such requirement limits the number of wavelengths that can be exploited in a WDM network up to the size of the resolvable wavelength set of optical transceivers, which is very limited with current technology. In this paper we observe that this requirement is actually an overkill. To realize a communication topology, physical or logical, it is sufficient that the tunable range of the transmitter at each station covers all the wavelengths of the receivers at its neighboring stations. This observation leads to the study of optimal wavelength assignment to minimize the tunability requirement while still guaranteeing that each receiver has a unique wavelength channel. This optimization problem is shown to NP-complete in general and approximation algorithms with provable performance guarantees are presented. When the communication topologies are complete graphs, de Bruijin digraphs, Kautz digraphs, shuffle or rings, the optimal solutions are provided. Finally, we present tight lower bounds when the communication topology is a hypercube.

Optical burst switching: the next IT revolution worth multiple billions dollars?

All-optical Internet may one day come true, due to the explosive bandwidth requirement, and advances of enabling optical communication techniques. And exactly NOW we are at the turning point. We study one possible optical packet switching technique-optical burst switching. We present the overall network protocol, enabling techniques, architectures, switching cores and performance evaluations.

Optimal routing based on super topology in hypercube WDM networks

Traditionally the routing in passive optical networks is based on an embedded regular virtual topology. However one important fact that has been neglected in the past is that the wavelength assignment to transceivers actually creates additional (logical) links not present in the virtual topology. Such side effect can be utilized to significantly reduce the number of hops between a pair of stations. This observation leads to the concept of super topology. This paper considers the hypercube as the embedded virtual topology. The ideas contained here are easily applicable to networks employing other virtual topologies as well. We present the structure of the super topology, the optimal routing algorithm, the distance between any pair of stations and the diameter in the super topology.

Optimal Routing Based on Super Topology in Optical Parallel Interconnect

Traditionally the routing in optical parallel interconnect is based on an embedded virtual topology. However, one important fact that has been neglected in the past is that the wavelength assignment to transceivers actually creates additional (logical) links not present in the virtual topology. Such a side-effect can be utilized to significantly reduce the number of hops between a pair of processors. This observation leads to the concept of super topology. This paper considers the hypercube as the embedded virtual topology. The ideas contained here are easily applicable to optical parallel interconnects employing other virtual topologies as well. We present a general framework for embedding a regular topology, the structure of the super topology, the optimal routing algorithm, the distance between any pair of processors and the diameter in the super topology.