Mapping constrained optimization problems to quantum annealing with application to fault diagnosis

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.Comment: 22 pages, 4 figure

Wavelength assignment algorithms for WDM optical networks

The explosive growth of the Internet and bandwidth-intensive applications such as video-ondemand and multimedia conferences require high-bandwidth networks. The current highspeed electronic networks cannot provide such capacity. Optical networks offer much higher bandwidth than traditional networks. When employed with the wavelength division multiplexing (WDM) technology, they can provide the huge bandwidth needed. The tree of rings is a popular topology which can often be found in WDM networks. In this thesis, we first study wavelength assignment (WA) algorithms for trees of rings. A tree o

Algorithms for wavelength assignment and call control in optical networks

Routing and channel assignment is a fundamental problem in computer/communication networks. In wavelength division multiplexing (WDM) optical networks, the problem is called routing and wavelength assignment or routing and path coloring (RPC) problem: given a set of connection requests, find a routing path to connect each request and assign each path a wavelength channel (often called a color) subject to certain constraints. One constraint is the distinct channel assignment: the colors (channels) of the paths in the same optical fiber must be distinct. Another common constraint is the channel continuity: a path is assigned a single color. When a path may be assigned different colors on different fibers, the RPC problem is known as the routing and call control (RCC) problem. When the routing paths are given as part of the problem input, the RPC and RCC problems are called the path coloring and call control problems, respectively. Major optimization goals for the above problems include to minimize the number of colors for realizing a given set of requests and to maximize the number of accommodated requests using a given number of colors. Those optimization problems are NP-hard for most network topologies, even for simple networks like rings and trees of depth one. In this thesis, we make the following contributions. (1) We give better approximation algorithms which use at most 3L (L is the maximum number of paths in a fiber) colors for the minimum path coloring problem in trees of rings. The 3L upper bound is tight since there are instances requiring 3L colors. We also give better approximation algorithms for the maximum RPC problem in rings. (2) We develop better algorithms for the minimum and maximum RPC problems on multi-fiber networks. (3) We develop better algorithms for the call control problem on simple topologies. (4) We develop carving-decomposition based exact algorithms for the maximum edge-disjoint paths problem in general topologies. We develop and implement tools for computing optimal branch/carving decompositions of planar graphs to provide a base for the branch/carving-decomposition based algorithms. These tools are of independent interests

Airflow and wood drying models for woodkilns

Airflow and heat/mass transfer in a woodkiln are simulated numerically. The uniformity of drying and the quality of the wood in a kiln are strongly influenced by the airflow. A numerical model that simulates the airflow distribution is described and applied to solve the flow distribution in a kiln. The influences of the gaps between lumber pieces and the unevenness of lumber height on the velocity distribution and heat/mass transfer in the woodkiln are investigated numerically. A mathematical model for heat and mass transfer during the wood drying process is presented. The influence of kiln temperature, humidity and transport properties of wood is numerically investigated. The three key parameters in the model are moisture content M , temperature T and total pressure P in the gaseous phase. The results are compared with drying rate experiments carried out by Forintek Canada Corporation. Numerical model predictions are in satisfactory agreement with experimental results. Airflow and wood drying models are coupled to carry out a complete calculation. The model will constitute a powerful tool to optimize kiln design and to help operators improve kiln operations without entailing major new costs.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat

Empirical Study on Branchwidth and Branch Decomposition of Planar Graphs

We propose efficient implementations of Seymour and Thomas algorithm which, given a planar graph and an in-teger β, decides whether the graph has the branchwidth at least β. The computational results of our implementations show that the branchwidth of a planar graph can be com-puted in a practical time and memory space for some in-stances of size about one hundred thousand edges. Previous studies report that a straightforward implementation of the algorithm is memory consuming, which could be a bottle-neck for solving instances with more than a few thousands edges. Our results suggest that with efficient implementa-tions, the memory space required by the algorithm may not be a bottleneck in practice. Applying our implementations, an optimal branch decomposition of a planar graph of prac

Lewis Acid-Mediated Room-Temperature Cascade Reaction of 3‑Hydroxyisoindolin-1-one with Alkynes

An efficient and mild synthesis of a variety of 3-(2-oxopropyl)-isoindolinone derivatives via a BF₃·Et₂O catalyzed cascade reaction among 3-hydroxyisoindolin-1-one and phenylacetylene was achieved. Various isoindolinone derivatives were obtained in good to excellent yields. The process, which avoided several drawbacks such as the requirement of concentrated protic acids and metal catalysts, protecting group of nitrogen, high temperature, and multistep synthesis, includes C­(sp³)–OH cleavage, C–C coupling, and hydration of alkyne