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Ride-share systems, which aim to bring together travelers with similar itineraries and time schedules, may provide significant societal and environmental benefits by reducing the number of cars used for personal travel and improving the utilization of available seat capacity. Effective and efficient optimization technology that matches drivers and riders in real-time is one of the necessary components for a successful ride-share system. The research conducted in this dissertation formally defines dynamic or real-time ride-sharing, identifies optimization problems for finding best sets of ride-share matches in a number of operational scenarios, develops approaches for solving ride-share optimization problems, and tests the concepts via a simulation study of work trips in the Atlanta metropolitan area. The first chapter introduces the motivation of the ride-sharing problem and briefly defines the dynamic ride-sharing system. In Chapter 2, we systematically outline the optimization challenges that arise when developing technology to support ride-sharing and survey the related operations research models in academic literature. In Chapter 3, we develop optimization-based approaches for finding ride-share matches in a standard problem setting, with the goal of minimizing the total system-wide vehicle miles incurred by system users. To assess the merits of our methods we present a simulation study based on 2008 travel demand data from metropolitan Atlanta. The simulation results indicate that the use of sophisticated optimization methods instead of simple greedy matching rules substantially improves the performance of ride-sharing systems. Furthermore, even with relatively low participation rates, it appears that sustainable populations of dynamic ride-sharing participants may be possible even in relatively sprawling urban areas with many employment centers. In Chapter 4, we consider a more sophisticated ride-share setting where participants may be unlikely to accept ride-share matches if they are not stable. Generically, a set of matches between riders and drivers is defined as stable if no rider and driver, currently matched to others, would prefer to be matched together. This notion of stability is similar to that of the stable marriage problem. We develop notions of stable ride-share matching in a variety of settings, and develop approaches for finding stable (or nearly-stable) solutions. Computational results are used to compare system performance under various levels of matching stability. A system with unstable matching assignments is simulated over two months in which participants are likely to reject the system's assignment if a private arrangement between individuals could bring better benefits. The simulation results indicate that the total savings generated by a ride-sharing system deteriorate with unstable matching assignments and that enforcing stability constraints in matching models is beneficial. In Chapter 5, we consider another set of more sophisticated ride-share matching settings where participants are not assumed to accept each match to which they are assigned. In such settings, it may be useful to present users with a menu of possible ride-share matches from which they can choose. We develop models and solution approaches to jointly present multiple options to participants based on a complete bipartite graph structure. This research could serve as a building block for future work on the dynamic ride-sharing problem.

Current software engineering topics such as clone detection and service selection need to improve the capability of detection process and selection process. The clone detection is the process of finding duplicated code through the system for several purposes such as removal of repeated portions as maintenance part of legacy system. Service selection is the process of finding the appropriate web service which meets the consumer’s request. Both problems can be converted into a matching problem. Matching process forms an essential part of software engineering activities. In this research, a well-known mathematical algorithm Stable Marriage Problem (SMP) and its variations are investigated to fulfil the purposes of matching processes in software engineering area. We aim to provide a competitive matching algorithm that can help to detect cloned software accurately and ensure high scalability, precision and recall. We also aim to apply matching algorithm on incoming request and service profile to deal with the web service as a clever independent object so that we can allow the services to accept or decline requests (equal opportunity) rather than the current state of service selection (search-based), in which service lacks of interacting as an independent candidate. In order to meet the above aims, the traditional SMP algorithm has been extended to achieve the cardinality of many-to-many. This adaptation is achieved by defining the selective strategy which is the main engine of the new adaptations. Two adaptations, Dual-Proposed and Dual-Multi-Allocation, have been proposed to both service selection and clone detection process. The proposed approach (SMP-based) shows very competitive results compare to existing software clone approaches, especially in identifying type 3 (copy with further modifications such update, add and delete statements) of cloned software. It performs the detection process with a relatively high precision and recall compare to the CloneDR tool and shows good scalability on a middle sized program. For service selection, the proposed approach has several advantages such as service protection and service quality. The services gain equal opportunity against the incoming requests. Therefore, the intelligent service interaction is achieved, and both stability and satisfaction of the candidates are ensured. This dissertation contributes to several contributions firstly, the new extended SMP algorithm by introducing selective strategy to accommodate many-to-many matching problems, to improve overall features. Secondly, a new SMP-based clone detection approach to detect cloned software accurately and ensures high precision and recall. Ultimately, a new SMPbased service selection approach allows equal opportunity between services and requests. This led to improve service protection and service quality. Case studies are carried out for experiments with the proposed approach, which show that the new adaptations can be applied effectively to clone detection and service selection processes with several features (e.g. accuracy). It can be concluded that the match based approach is feasible and promising in software engineering domain.

It is the aim of this paper to review some of the work done on stable matching, and on stable marriage problems in particular. Variants of the stable marriage problem will be considered, and the similarities and differences from a mathematical point of view will be highlighted. The correlation between preference and stability is a main theme, and the way in which diluted or incomplete preferences affect stability is explored. Since these problems have a wide range of practical applications, it is of interest to develop useful algorithms for the derivation of solutions. Time-complexity is a key factor in designing computable algorithms, making work load a strong consideration for practical purposes. Average and worst-case complexity are discussed. The number of different solutions that are possible for a given problem instance is surprising, and counter-intuitive. This leads naturally to a study of the solution sets and the lattice structure of solutions that emerges for any stable marriage problem. Many theorems derive from the lattice structure of stable solutions and it is shown that this can lead to the design of more efficient algorithms. The research on this topic is well established, and many theorems have been proved and published, although some published proofs have omitted the detail. In this paper, the author selects some key theorems, providing detailed proofs or alternate proofs, showing the mathematical richness of this field of study. Various applications are discussed, particularly with relevance to the social sciences, although mention is made of applications in computer science, game theory, and economics. The current research that is evident in this subject area, by reference to technical papers in periodicals and on the internet, suggests that it will remain a key topic for some time to come. / MATHEMATICAL SCIENCES / MSC (MATHEMATICS)

“The Stable marriage problem (SMP) is basically the problem of finding a stable matchingbetween two sets of persons, the men and the women, where each person in every group has a listcontaining every person that belongs to other group ordered by preference. The first ones to discovera stable solution for the problem were D. Gale and G.S. Shapley. Today the problem and most of itsvariations have been studied by many researchers, and for most of them polynomial time algorithmsdo not exist. Lately genetic algorithms have been used to solve such problems and have oftenproduced better solutions than specialized polynomial algorithms. In this thesis we study and showthat the Stable marriage problem has a number of important real-world applications. It theexperimentation, we model the original problem and one of its variations and show the benefits ofusing genetic algorithms for solving the SMP.” / Program: Magisterutbildning i informatik

Stable matchings were introduced in 1962 by David Gale and Lloyd Shapley to study the college admissions problem. The seminal work of Gale and Shapley has motivated hundreds of research papers and found applications in many areas of mathematics, computer science, economics, and even medicine. This thesis studies stable matchings in graphs and hypergraphs. We begin by introducing the work of Gale and Shapley. Their main contribution was the proof that every bipartite graph has a stable matching. Our discussion revolves around the Gale-Shapley algorithm and highlights some of the interesting properties of stable matchings in bipartite graphs. We then progress to non-bipartite graphs. Contrary to bipartite graphs, we may not be able to find a stable matching in a non-bipartite graph. Some of the work of Irving will be surveyed, including his extension of the Gale-Shapley algorithm. Irving's algorithm shows that many of the properties of bipartite stable matchings remain when the general case is examined. In 1991, Tan showed how to extend the fundamental theorem of Gale and Shapley to non-bipartite graphs. He proved that every graph contains a set of edges that is very similar to a stable matching. In the process, he found a characterization of graphs with stable matchings based on a modification of Irving's algorithm. Aharoni and Fleiner gave a non-constructive proof of Tan's Theorem in 2003. Their proof relies on a powerful topological result, due to Scarf in 1965. In fact, their result extends beyond graphs and shows that every hypergraph has a fractional stable matching. We show how their work provides new and simpler proofs to several of Tan's results. We then consider fractional stable matchings from a linear programming perspective. Vande Vate obtained the first formulation for complete bipartite graphs in 1989. Further, he showed that the extreme points of the solution set exactly correspond to stable matchings. Roth, Rothblum, and Vande Vate extended Vande Vate's work to arbitrary bipartite graphs. Abeledo and Rothblum further noticed that this new formulation can model fractional stable matchings in non-bipartite graphs in 1994. Remarkably, these formulations yield analogous results to those obtained from Gale-Shapley's and Irving's algorithms. Without the presence of an algorithm, the properties are obtained through clever applications of duality and complementary slackness. We will also discuss stable matchings in hypergraphs. However, the desirable properties that are present in graphs no longer hold. To rectify this problem, we introduce a new ``majority" stable matchings for 3-uniform hypergraphs and show that, under this stronger definition, many properties extend beyond graphs. Once again, the linear programming tools of duality and complementary slackness are invaluable to our analysis. We will conclude with a discussion of two open problems relating to stable matchings in 3-uniform hypergraphs.

Stable matchings were introduced in 1962 by David Gale and Lloyd Shapley to study the college admissions problem. The seminal work of Gale and Shapley has motivated hundreds of research papers and found applications in many areas of mathematics, computer science, economics, and even medicine. This thesis studies stable matchings in graphs and hypergraphs. We begin by introducing the work of Gale and Shapley. Their main contribution was the proof that every bipartite graph has a stable matching. Our discussion revolves around the Gale-Shapley algorithm and highlights some of the interesting properties of stable matchings in bipartite graphs. We then progress to non-bipartite graphs. Contrary to bipartite graphs, we may not be able to find a stable matching in a non-bipartite graph. Some of the work of Irving will be surveyed, including his extension of the Gale-Shapley algorithm. Irving's algorithm shows that many of the properties of bipartite stable matchings remain when the general case is examined. In 1991, Tan showed how to extend the fundamental theorem of Gale and Shapley to non-bipartite graphs. He proved that every graph contains a set of edges that is very similar to a stable matching. In the process, he found a characterization of graphs with stable matchings based on a modification of Irving's algorithm. Aharoni and Fleiner gave a non-constructive proof of Tan's Theorem in 2003. Their proof relies on a powerful topological result, due to Scarf in 1965. In fact, their result extends beyond graphs and shows that every hypergraph has a fractional stable matching. We show how their work provides new and simpler proofs to several of Tan's results. We then consider fractional stable matchings from a linear programming perspective. Vande Vate obtained the first formulation for complete bipartite graphs in 1989. Further, he showed that the extreme points of the solution set exactly correspond to stable matchings. Roth, Rothblum, and Vande Vate extended Vande Vate's work to arbitrary bipartite graphs. Abeledo and Rothblum further noticed that this new formulation can model fractional stable matchings in non-bipartite graphs in 1994. Remarkably, these formulations yield analogous results to those obtained from Gale-Shapley's and Irving's algorithms. Without the presence of an algorithm, the properties are obtained through clever applications of duality and complementary slackness. We will also discuss stable matchings in hypergraphs. However, the desirable properties that are present in graphs no longer hold. To rectify this problem, we introduce a new ``majority" stable matchings for 3-uniform hypergraphs and show that, under this stronger definition, many properties extend beyond graphs. Once again, the linear programming tools of duality and complementary slackness are invaluable to our analysis. We will conclude with a discussion of two open problems relating to stable matchings in 3-uniform hypergraphs.

It is the aim of this paper to review some of the work done on stable matching, and on stable marriage problems in particular. Variants of the stable marriage problem will be considered, and the similarities and differences from a mathematical point of view will be highlighted. The correlation between preference and stability is a main theme, and the way in which diluted or incomplete preferences affect stability is explored. Since these problems have a wide range of practical applications, it is of interest to develop useful algorithms for the derivation of solutions. Time-complexity is a key factor in designing computable algorithms, making work load a strong consideration for practical purposes. Average and worst-case complexity are discussed. The number of different solutions that are possible for a given problem instance is surprising, and counter-intuitive. This leads naturally to a study of the solution sets and the lattice structure of solutions that emerges for any stable marriage problem. Many theorems derive from the lattice structure of stable solutions and it is shown that this can lead to the design of more efficient algorithms. The research on this topic is well established, and many theorems have been proved and published, although some published proofs have omitted the detail. In this paper, the author selects some key theorems, providing detailed proofs or alternate proofs, showing the mathematical richness of this field of study. Various applications are discussed, particularly with relevance to the social sciences, although mention is made of applications in computer science, game theory, and economics. The current research that is evident in this subject area, by reference to technical papers in periodicals and on the internet, suggests that it will remain a key topic for some time to come. / MATHEMATICAL SCIENCES / MSC (MATHEMATICS)