Let <b>A</b> and <b>B</b> be finite sets with |<b>A</b>|=<i>n</i> and |<b>B</b>|=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)-<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> such that for any <b>X</b> &#8838; <b>A</b> with |<b>X</b>|=<i>w</i>, there exists at least one ? &#8712; <i>F</i> such that ? is one-to-one when restricted to <b>X</b>. Perfect hash families are basic combinatorial structures and they have played important roles in Computer Science in areas such as database management, operating systems, and compiler constructions. Such hash families are used for memory efficient storage and fast retrieval of items such as reserved words in programming languages, command names in interactive systems, or commonly used words in natural languages. More recently, perfect hash families have found numerous applications to cryptography, for example, to broadcast encryption schemes, secret sharing, key distribution patterns, visual cryptography, cover-free families and secure frameproof codes. In this thesis, we survey constructions and applications of perfect hash families. For constructions, we divided the results into three parts, depending on underlying structure and properties of the constructions: combinatorial structures, linear functionals, and algebraic structures. For applications, we focus on those related to cryptography.

In this thesis we present a novel algorithm, <I>HyperCleaning*</I>, for effectively inferring phylogenetic trees. The method is based on the quartet method paradigm and is guaranteed to recover the best supported edges of the underlying phylogeny based on the witness quartet set. This is performed efficiently using a collapsing mechanism that employs memory/time tradeoff to ensure no loss of information. This enables <I>HyperCleaning*</I> to solve the relaxed version of the Maximum-Quartet-Consistency problem feasibly, thus providing a valuable tool for inferring phylogenies using quartet based analysis.

Combinatorial auctions (CAs) are an important mechanism for allocating multiple items while allowing agents to specify preferences over bundles of items. In order to communicate these preferences, agents submit bids, which consist of one or more items and a value indicating the agent’s preference for these items. The process of determining the allocation of items is known as the winner determination problem (WDP). WDP for CAs is known to be NP-complete in the general case. We consider two distinct graph representations of a CA; the bid graph and the item graph. In a bid graph, vertices represent bids, and two vertices are adjacent if and only if the bids share items in common. In an item graph, each vertex represents a unique item, there is a vertex for each item, and any bid submitted by any agent must induce a connected subgraph of the item graph. We introduce a new definition of combinatorial auction equivalence by declaring two CAs equivalent if and only if their bid graphs are isomorphic. Parameterized complexity theory can be used to further distinguish between NP-hard problems. In order to make use of parameterized complexity theory in the investigation of a problem, we aim to find one or more parameters that describe some aspect of the problem such that if we fix these parameters, then either the problem is still hard (fixed-parameter intractable), or the problem can be solved in polynomial time (fixed-parameter tractable). We analyze WDP using bid graphs from within the formal scope of parameterized complexity theory. This approach has not previously been used to analyze WDP for CAs, although it has been used to solve set packing, which is related to WDP for CAs and is discussed in detail. We investigate a few parameterizations of WDP; some of the parameterizations are shown to be fixed-parameter intractable, while others are fixed-parameter tractable. We also analyze WDP when the graph class of a bid graph is restricted. We also discuss relationships between item graphs and bid graphs. Although both graphs can represent the same problem, there is little previous work analyzing direct relationships between them. Our discussion on these relationships begins with a result by Conitzer et al. [7], which focuses on the item graph representation and its treewidth, a property of a graph that measures how close the graph is to a tree. From a result by Gavril, if an item graph has treewidth one, then the bid graph must be chordal [16]. To apply the other direction of Gavril’s theorem, we use our new definition of CA equivalence. With this new definition, Gavril’s result shows that if a bid graph of a CA is chordal, then we can construct an item graph that has treewidth one for some equivalent CA.

One of the simplest, but still NP-hard, routing problems is the Traveling Salesman Problem (TSP). In the TSP, one is given a set of cities and a way of measuring the distance between cities. One has to find the shortest tour that visits all cities exactly once and returns back to the starting city. In state-of-the-art algorithms, they all assume that a complete graph is given as an input. However, for very large graphs, generating all edges in a complete graph, which corresponds to finding shortest paths for all city pairs, could be time-consuming. This is definitely a major obstacle for some real-life applications, especially when the tour needs to be generated in real-time. The objective, in this thesis, is to find a near-optimal TSP tour with a reduced set of edges in the complete graph. In particular, the following problems are investigated: which subset of edges can be produced in a shorter time comparing to the time for generating the complete graph? Is there a subset of edges in the complete graph that results in a better near-optimal tour than other sets? With a non-complete graph, which improvement algorithms work better? In this thesis, we study six algorithms to generate subsets of edges in a complete graph. To evaluate the proposed algorithms, extensive experiments are conducted with the well-known TSP data in a TSP library. In these experiments, we evaluate these algorithms in terms of tour quality, time and scalability.

<p>For at least two thousand years, voting has been used as one of the most effective ways to aggregate people's ordinal preferences. In the last 50 years, the rapid development of Computer Science has revolutionize every aspect of the world, including voting. This motivates us to study (1) <bold>conceptually, how computational thinking changes the traditional voting theory</bold>, and (2) <bold>methodologically, how to better use voting for preference/information aggregation with the help of Computer</p><p>Science</bold>.</p><p>My Ph.D. work seeks to investigate and foster the interplay between Computer Science and Voting Theory. In this thesis, I will discuss two specific research directions pursued in my Ph.D. work, one for each question asked above. The first focuses on investigating how computational thinking affects the game-theoretic aspects of voting. More precisely, I will discuss the rationale and possibility of using computational complexity to protect voting from a type of strategic behavior of the voters, called <italic>manipulation</italic>. The second studies a voting setting called <italic>Combinatorial Voting</italic>, where the set of alternative is exponentially large and has a combinatorial structure. I will focus on the design and analysis of novel voting rules for combinatorial voting that balance computational efficiency and the expressivity of the voting language, in light of some recent developments in Artificial Intelligence.</p> / Dissertation

Optimization problems are divided into numerical optimization problems and combinatorial optimization problems. Genetic algorithms (GAs) are applied to solve optimization problems widely. GAs with multi-parent crossover are often used to solve numerical optimization problems. However, no effective multi-parent crossover is used for combinatorial optimization problems. Partially mapped crossover (PMX) is the most popular crossover for combinatorial optimization problems. In this thesis, we propose multi-parent partially mapped crossover (MPPMX). A large amount of experimental results show that the improvement ratio of MPPMX reaches 38.63 % over PMX. The p-values of t-test on the difference between MPPMX and PMX range from 10-6 to 10-14, which indicates the significant improvement of MPPMX over PMX.

In recent year, a lot of scholar try to generate test sets for combinatorial strategy automatically. But these algorithms based on combinatorial strategy don¡¦t consider conflicts of input parameter model. A conflict exists when the result of combining two or more values of different parameter dose not make sense. Thus, invalid sub-combinations may be included in test cases in the test suite, and these are useless to us. Besides, these algorithms all directly generate all test cases once, in other words, it is unable to utilize test cases generated at present to feedback and revise the algorithm, so it is easy to generate useless combinations. So, this paper proposes new test generation algorithm for combinatorial testing based on constraint satisfaction problem(CSP) to solve problem which invalid sub-combinations may be included in test cases, and we can add constraints flexibly during generating test cases to avoid generate useless or repeated combinations. The experimental result indicate that our algorithm perform well, with respect to the amount of time required for test generation, otherwise, we can generate conflict-free test cases directly.

Electronic commerce is becoming more important day by day. Many transactions and business are done electronically and many people do not want paper work anymore. When a firm wants to buy raw materials or components, it announces its need to related websites or in the newspapers. Similar demands and announcements can be seen almost everywhere nowadays. In this way, it needs to perform fast and reliable auctions as much as possible. On the other hand, buyers not only consider cost but also consider a lot of different aspects like quality, warranty period, lead time etc when they want to purchase something. This situation leads to more complex problems in the purchasing process. As a consequence, some researchers started to consider auction mechanisms that support bids characterized by several attributes in addition to the price (quality of the product, quantity, terms of delivery, quality of the supplier etc.). These are referred to as multi-attribute combinatorial auctions. In this thesis, Combinatorial Auctions are analyzed. Single-attribute multi-unit, multi-attribute multi-unit combinatorial auction models are studied and an interactive method is applied for solving the multi-attribute multi-unit combinatorial auction problem.

ABSTRACT PERFORMANCE MEASUREMENT IN MULTI OBJECTIVE COMBINATORIAL OPTIMIZATION Bozkurt, Bilge M.Sc., Department of Industrial Engineering Supervisor: Prof. Dr. Murat K&ouml / ksalan September 2007, 96 pages In this study we address the problem of measuring the quality of different sets of nondominated solutions obtained by different approaches in multi objective combinatorial optimization (MOCO). We propose a new measure that quantitatively compares the sets of nondominated solutions, without needing an efficient frontier. We develop the measure for bi-criteria and more than two criteria cases separately. Rather than considering only the supported solutions in the evaluation, the measure captures both supported and unsupported solutions through utilizing weighted Tchebycheff function characteristics. We also adapt this method for determining the neighborhood relations on the weight space for both bi-criteria and more than two criteria cases. We check the consistency of the neighborhood assumption on the objective space with the neighborhood relations on the weight space by this measure and obtain highly good results. Keywords: Multi objective combinatorial optimization, performance measurement

We propose a generic algorithm based on branch-and-bound to generate all efficient solutions of multiobjective combinatorial optimization (MOCO) problems. We present an algorithm specific to multiobjective 0-1 Knapsack Problem based on the generic algorithm. We test the performance of our algorithm on randomly generated sample problems against IBM ILOG CPLEX and we obtain better performance using a problem specific algorithm. We develop a heuristic algorithm by incorporating memory limitations at the expense of solution quality to overcome memory issues of the exact algorithm.