Unconstraining Graph-Constrained Group Testing

In network tomography, one goal is to identify a small set of failed links in a network using as little information as possible. One way of setting up this problem is called graph-constrained group testing. Graph-constrained group testing is a variant of the classical combinatorial group testing problem, where the tests that one is allowed are additionally constrained by a graph. In this case, the graph is given by the underlying network topology. The main contribution of this work is to show that for most graphs, the constraints imposed by the graph are no constraint at all. That is, the number of tests required to identify the failed links in graph-constrained group testing is near-optimal even for the corresponding group testing problem with no graph constraints. Our approach is based on a simple randomized construction of tests. To analyze our construction, we prove new results about the size of giant components in randomly sparsified graphs. Finally, we provide empirical results which suggest that our connected-subgraph tests perform better not just in theory but also in practice, and in particular perform better on a real-world network topology

Quality of Transmission Aware Optical Networking Using Enhanced Gaussian Noise Model

We present a new joint routing, wavelength, and power allocation method for optical network planning. The introduced gradient-based convex optimization approach has a lower computational complexity, compared to common linear programming techniques, suitable for both static as well as time-critical dynamic network planning with fast convergence requirement. The proposed scheme takes physical-layer impairments into account, using the enhanced Gaussian noise nonlinear model. In contrast to methods exploiting the theoretical full link spectrum utilization assumption (fully occupied fiber-optic C-hand spectrum), we focus on maximizing the network achievable rate and minimum signal-to-noise ratio (SNR) margin of networks with partial spectrum utilization in their links, relevant to the majority of empirical metro network scenarios. According to numerical results, the network achievable rate can be improved around 17% by performing power optimization over the individual launch power of network lightpaths compared to optimizing a single flat (equal) launch power for all the lightpaths. Moreover, the minimum SNR margin of the simulated network is improved by about 23 dB. Finally, it is observed that maximizing the network minimum SNR margin needs the launch power of each lightpath to be proportional to the total nonlinear interference noise efficiency influencing the lightpath

Resource allocation and scalability in dynamic wavelength-routed optical networks.

This thesis investigates the potential benefits of dynamic operation of wavelength-routed optical networks (WRONs) compared to the static approach. It is widely believed that dynamic operation of WRONs would overcome the inefficiencies of the static allocation in improving resource use. By rapidly allocating resources only when and where required, dynamic networks could potentially provide the same service that static networks but at decreased cost, very attractive to network operators. This hypothesis, however, has not been verified. It is therefore the focus of this thesis to investigate whether dynamic operation of WRONs can save significant number of wavelengths compared to the static approach whilst maintaining acceptable levels of delay and scalability. Firstly, the wavelength-routed optical-burst-switching (WR-OBS) network architecture is selected as the dynamic architecture to be studied, due to its feasibility of implementation and its improved network performance. Then, the wavelength requirements of dynamic WR-OBS are evaluated by means of novel analysis and simulation and compared to that of static networks for uniform and non-uniform traffic demand. It is shown that dynamic WR-OBS saves wavelengths with respect to the static approach only at low loads and especially for sparsely connected networks and that wavelength conversion is a key capability to significantly increase the benefits of dynamic operation. The mean delay introduced by dynamic operation of WR-OBS is then assessed. The results show that the extra delay is not significant as to violate end-to-end limits of time-sensitive applications. Finally, the limiting scalability of WR-OBS as a function of the lightpath allocation algorithm computational complexity is studied. The trade-off between the request processing time and blocking probability is investigated and a new low-blocking and scalable lightpath allocation algorithm which improves the mentioned trade-off is proposed. The presented algorithms and results can be used in the analysis and design of dynamic WRONs