ABSTRACT: In the world of optimization, network optimization problems are considered fundamental to the practice. The work presented here focuses on the similarity constrained k shortest paths problem (SCKSPP) its formulation, and subsequent analysis. The formulation addresses several deficiencies which are present in prior works, and the analysis focuses on addressing major topics of feasibility and optimality which are not present in prior works. SCKSPP focuses around finding k simple paths from source to sink nodes while maintaining a pairwise dissimilarity. The purpose of this paper is to develop an underlying theory behind the SCKSPP to guide the development of an efficient solution method. The work itself is entirely theoretical; we give properties which use graph connectivity to describe the existence of feasible solutions, we demonstrate how objective function behavior affects uniqueness of the optimal solution, as well as other properties regarding feasibility and optimality. Furthermore, we show how specific graph structures allow smaller less computationally intensive problems to be solved, and then extrapolated to form optimal solutions of the larger problems. We also give several examples of similarity measures that incorporate context-specific constraints into already existing similarity constraints.

This book constitutes the refereed proceedings of the 13th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2007, held in Braga, Portugal. Coverage includes software verification, probabilistic model checking and markov chains, automata-based model checking, security, software and hardware verification, decision procedures and theorem provers, as well as infinite-state systems.

Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology. Table of Contents: List of Figures / List of Tables / Acknowledgments / Introduction / Graph Theory Basics / Classical Algorithms / Hierarchical Preprocessing-Dependent Approaches / Non-Hierarchical Preprocessing-Dependent Approaches / Analysis and Comparison of Approaches / Conclusions / Bibliography / Authors' Biographies

This book constitutes the refereed proceedings of the 15th Annual International Conference on Research in Computational Molecular Biology, RECOMB 2011, held in Vancouver, Canada, in March 2011. The 43 revised full papers were carefully reviewed and selected from 153 submissions. The papers cover a wide range of topics including molecular sequence analysis; recognition of genes and regulatory elements; molecular evolution; gene expression; biological networks; sequencing and genotyping technologies; genomics; population, statistical genetics; systems biology; imaging; computational proteomics; molecular structural biology.

In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.

Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).

Multiple Criteria Decision Analysis: State of the Art Surveys provides survey articles and references of the seminal or state-of-the-art research on MCDA. The material covered ranges from the foundations of MCDA, over various MCDA methodologies (outranking methods, multiattribute utility and value theories, non-classical approaches) to multiobjective mathematical programming, MCDA applications, and software. This vast amount of material is organized in 8 parts, with a total of 25 chapters. More than 2000 references are listed.

This book constitutes the refereed proceedings of the 8th Annual European Symposium on Algorithms, ESA 2000, held in Saarbrcken, Germany in September 2000. The 39 revised full papers presented together with two invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are parallelism, distributed systems, approximation, combinatorial optimization, computational biology, computational geometry, external-memory algorithms, graph algorithms, network algorithms, online algorithms, data compression, symbolic computation, pattern matching, and randomized algorithms.