Algorithms and Dynamic Data Structures for Basic Graph Optimization Problems.

Graph optimization plays an important role in a wide range of areas such as computer graphics, computational biology, networking applications and machine learning. Among numerous graph optimization problems, some basic problems, such as shortest paths, minimum spanning tree, and maximum matching, are the most fundamental ones. They have practical applications in various fields, and are also building blocks of many other algorithms. Improvements in algorithms for these problems can thus have a great impact both in practice and in theory. In this thesis, we study a number of graph optimization problems. The results are mostly about approximation algorithms solving graph problems, or efficient dynamic data structures which can answer graph queries when a number of changes occur. Much of my work focuses on the dynamic subgraph model in which there is a fixed underlying graph and every vertex can be flipped "on" or "off". The queries are based on the subgraph induced by the "on" vertices. Our results make significant improvements to the previous algorithms of these problems. The major results are listed below. Approximate Matching. We give the first linear time algorithm for computing approximate maximum weighted matching for arbitrarily small approximation ratio. d-failure Connectivity Oracle. For an undirected graph, we give the first space efficient data structure that can answer connectivity queries between any pair of vertices avoiding d other failed vertices in time polynomial in d and log n. (Max, Min)-Matrix Multiplication. We give a faster algorithm for the (max, min)-matrix multiplication problem, which has a direct application to the all- pairs bottleneck paths (APBP) problem. Dual-failure Distance Oracle. We construct the data structure for a given directed graph of nearly quadratic space which can efficiently answer distance and shortest path queries in the presence of two node or link failures. Dynamic Subgraph Connectivity. We give the first subgraph connectivity structure with worst-case sublinear time bounds for both updates and queries. Bounded-leg Shortest Path. We give an algorithm for preprocessing a directed graph in nearly cubic time in order to answer approximate bounded-leg distance and bounded-leg shortest path queries in merely sub-logarithmic time.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89641/1/duanran_1.pd

Primal Cutting Plane Methods for the Traveling Salesman Problem

Most serious attempts at solving the traveling salesman problem (TSP) are based on the dual fractional cutting plane approach, which moves from one lower bound to the next. This thesis describes methods for implementing a TSP solver based on a primal cutting plane approach, which moves from tour to tour with non-degenerate primal simplex pivots and so-called primal cutting planes. Primal cutting plane solution of the TSP has received scant attention in the literature; this thesis seeks to redress this gap, and its findings are threefold. Firstly, we develop some theory around the computation of non-degenerate primal simplex pivots, relevant to general primal cutting plane computation. This theory guides highly efficient implementation choices, a sticking point in prior studies. Secondly, we engage in a practical study of several existing primal separation algorithms for finding TSP cuts. These algorithms are all conceptually simpler, easier to implement, or asymptotically faster than their standard counterparts. Finally, this thesis may constitute the first computational study of the work of Fleischer, Letchford, and Lodi on polynomial-time separation of simple domino parity inequalities. We discuss exact and heuristic enhancements, including a shrinking-style heuristic which makes the algorithm more suitable for application on large-scale instances. The theoretical developments of this thesis are integrated into a branch-cut-price TSP solver which is used to obtain computational results on a variety of test instances

A framework for structuring prerequisite relations between concepts in educational textbooks

In our age we are experiencing an increasing availability of digital educational resources and self-regulated learning. In this scenario, the development of automatic strategies for organizing the knowledge embodied in educational resources has a tremendous potential for building personalized learning paths and applications such as intelligent textbooks and recommender systems of learning materials. To this aim, a straightforward approach consists in enriching the educational materials with a concept graph, i.a. a knowledge structure where key concepts of the subject matter are represented as nodes and prerequisite dependencies among such concepts are also explicitly represented. This thesis focuses therefore on prerequisite relations in textbooks and it has two main research goals. The first goal is to define a methodology for systematically annotating prerequisite relations in textbooks, which is functional for analysing the prerequisite phenomenon and for evaluating and training automatic methods of extraction. The second goal concerns the automatic extraction of prerequisite relations from textbooks. These two research goals will guide towards the design of PRET, i.e. a comprehensive framework for supporting researchers involved in this research issue. The framework described in the present thesis allows indeed researchers to conduct the following tasks: 1) manual annotation of educational texts, in order to create datasets to be used for machine learning algorithms or for evaluation as gold standards; 2) annotation analysis, for investigating inter-annotator agreement, graph metrics and in-context linguistic features; 3) data visualization, for visually exploring datasets and gaining insights of the problem that may lead to improve algorithms; 4) automatic extraction of prerequisite relations. As for the automatic extraction, we developed a method that is based on burst analysis of concepts in the textbook and we used the gold dataset with PR annotation for its evaluation, comparing the method with other metrics for PR extraction

Sparse flexibility structures: Design and application

Ph.DDOCTOR OF PHILOSOPH

Managerial tacit knowledge transfer and the mediating role of leader-member-exchange and cognitive style

The ability of an organisation to transfer knowledge is one of the key sources of competitive advantage for many of today’s organisations (Argote, 2000). New knowledge is created through interactions between explicit and tacit knowledge (Nonaka and Takeuchi, 1995). From the distinction between explicit and tacit knowledge made by Polanyi’s (1966), it is clear that the former can be transferred with relative ease, particularly using recent advances in information technology. Transfer of tacit knowledge on the other hand, requires social interactions with peers, colleagues, mentors and supervisor (Lahti et al, 2002; Cavusgil et al, 2003). Difficulties associated with this have been referred to as ‘internal stickiness’ (Szulanski, 1996) and is believed to be due to several factors. This study examines difficulties associated with the transfer of managerial tacit knowledge in the relationships involving supervisor and subordinates who work as managers in the Malaysian public sector. After examining previous literature in the field it is hypothesised that the stickiness of knowledge transfer may be associated with the quality of leader member exchange relationships, especially between leaders and their ‘in-group’ versus ‘out-group’ members. For example, in-group relationships are associated with higher levels of trust, respect and obligation compared with out-group relations. Another construct known to be associated with the quality of dyadic relationships is cognitive style (Armstrong, 1999). Cognitive style refers to individual differences in ways of perceiving, organising and processing information and differences in ways in which individuals solve problems, take decisions and relate to others. The research employed a quantitative approach using survey methods. Instruments used in the study included a measure of knowledge transfer stickiness (Szulanski, 1996), Leader Member Exchange (LMX7) (Graen and Uhl-Bien, 1995), Tacit Knowledge Inventory for Managers (TKIM) (Wagner and Sternberg, 1989) and the Cognitive Style Index (CSI) (Allinson and Hayes, 1996). The survey was administered to 1200 managers in the Malaysian Public Sector and 344 completed surveys were returned representing a response rate of 28.7%. Results from a final sample size of 300 managers comprising supervisors and their immediate subordinates are reported. The study successfully determined the relationship between knowledge transfer stickiness, LMX, cognitive style and managerial tacit knowledge. As expected, high-quality LMX leads to higher quality exchanges and concomitant improvements in the transfer of managerial tacit knowledge. Moreover, as hypothesised, individual differences and similarities in cognitive style also influence the transfer of tacit knowledge between supervisor and subordinate. Practical implications are given and recommendation made for future research

Model-based approaches to support process improvement in complex product development

The performance of product development processes is important to the commercial success of new products. The improvement of these processes is thus a strategic imperative for many engineering companies — the aero-engine is one example of a complex product for which market pressures necessitate ever-shorter development times. This thesis argues that process modelling and simulation can support the improvement of complex product development processes. A literature review identified that design process modelling is a well-established research area encompassing a diverse range of approaches. However, most existing tools and methods are not widely applied in industry. An extended case study was therefore conducted to explore the pragmatic utility of process modelling and simulation. It is argued that iteration is a key driver of design process behaviour which cannot be fully reflected in a mechanistic model. Understanding iteration can help select an appropriate representation for a given process domain and modelling objective. A model-based approach to improve the management of iterative design processes was developed. This approach shows that design process simulation models can support practice despite their limited fidelity. The modelling and simulation framework resulting from this work was enhanced for application to a wider range of process improvement activities. A robust and extensible software platform was also developed. The framework and software tool have made significant contribution to research projects investigating process redesign, process robustness and process optimisation. These projects are discussed to validate the framework and tool and to highlight their applicability beyond the original approach. The research results were disseminated in academia and industry — 72 copies of the software were distributed following requests in the first three months of its release