Browsing by Subject "Computational Complexity"
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Item Open Access Graph visualization toolkits(IEEE, 2002) Dogrusoz, U.; Feng, Q.; Madden, B.; Doorley, M.; Frick, A.The Graph Layout Toolkit and Graph Editor Toolkit, which provide a framework for graph visualization useful in a broad array of application areas are introduced. As such, an architectural overview of these tools is presented and discusses the challenges encountered during implementation and integration of theory and research results into such tools. In particular, the automatic graph layout and labeling algorithms and complexity management techniques are discussed. In addition, some examples of applications using these tools are presented.Item Open Access On the QAP polytope and a related inequality system(Bilkent University, 1997) Amcaoğlu, Beşir UThe Quadratic Assignment Problem is computationally one of the most dilficult NP-Hard problems. Recently, in 1996, Oguz introduced the so called ’triangle constraints’ into an extended model of the Travelling .Salesman problem (TSP) in an attempt to give a full description of the TSP polytope. In this study, we make use of these constraints in the context of the (Quadratic Assignment Problem (Q.AP). We discuss the relationships between the polytopes defined by the formulations with and without triangle constraints and we provide necessary and sufficient conditions for these constraints to give a full description of the QAP polytope. by-product of our analysis is that the triangle constraints suffice to define the QAP poly tope for n = 4.Item Open Access An overview of regression techniques for knowledge discovery(Cambridge University Press, 1999) Uysal, İ.; Güvenir, H. A.Predicting or learning numeric features is called regression in the statistical literature, and it is the subject of research in both machine learning and statistics. This paper reviews the important techniques and algorithms for regression developed by both communities. Regression is important for many applications, since lots of real life problems can be modeled as regression problems. The review includes Locally Weighted Regression (LWR), rule-based regression, Projection Pursuit Regression (PPR), instance-based regression, Multivariate Adaptive Regression Splines (MARS) and recursive partitioning regression methods that induce regression trees (CART, RETIS and M5).Item Open Access Quadratic assignment problem : linearizations and polynomial time solvable cases(Bilkent University, 2006) Erdoğan, GüneşThe Quadratic Assignment Problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this dissertation, we analyze the binary structure of the QAP and present new IP formulations. We focus on “flow-based” formulations, strengthen the formulations with valid inequalities, and report computational experience with a branch-and-cut algorithm. Next, we present new classes of instances of the QAP that can be completely or partially reduced to the Linear Assignment Problem and give procedures to check whether or not an instance is an element of one of these classes. We also identify classes of instances of the Koopmans-Beckmann form of the QAP that are solvable in polynomial time. Lastly, we present a strong lower bound based on Bender’s decomposition.