Rectilinear minimum link paths in two and higher dimensions

The thesis discusses algorithms for the minimum link path problem, which is a well known geometric path finding problem. The goal is to find a path that does the minimum number of turns amidst obstacles in a continuous space. We focus on the most classical variant, the rectilinear minimum link path problem, where the path and the obstacles are restricted to the directions of the coordinate axes. We study the rectilinear minimum link path problem in the plane and in the three-dimensional space, as well as in higher dimensional domains. We present several new algorithms for solving the problem in domains of varying dimension. For the planar case we develop a simple method that has the optimal O(n log n) time complexity. For three-dimensional domains we present a new algorithm with running time O(n^2 log^2 n), which is an improvement over the best previously known result O(n^2.5 log n). The algorithm can also be generalized to higher dimensions, leading to an O(n^(D-1) log^(D-1) n) time algorithm in D-dimensional domains. We describe the new algorithms as well as the data structures used. The algorithms work by maintaining a reachable region that is gradually expanded to form a shortest path map from the starting point. The algorithms rely on several efficient data structures: the reachable region is tracked by using a simple recursive space decomposition, and the region is expanded by a sweep plane method that uses a multidimensional segment tree

Structure-Aware Sampling: Flexible and Accurate Summarization

In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators and well-understood confidence bounds. Classic sample-based summaries, however, are designed for arbitrary subset queries and are oblivious to the structure in the set of keys. The particular structure, such as hierarchy, order, or product space (multi-dimensional), makes range queries much more relevant for most analysis of the data. Dedicated summarization algorithms for range-sum queries have also been extensively studied. They can outperform existing sampling schemes in terms of accuracy on range queries per summary size. Their accuracy, however, rapidly degrades when, as is often the case, the query spans multiple ranges. They are also less flexible - being targeted for range sum queries alone - and are often quite costly to build and use. In this paper we propose and evaluate variance optimal sampling schemes that are structure-aware. These summaries improve over the accuracy of existing structure-oblivious sampling schemes on range queries while retaining the benefits of sample-based summaries: flexible summaries, with high accuracy on both range queries and arbitrary subset queries

Reducing the expense of electronic structure calculations for larger molecules : optimized auxiliary basis sets, and system-specifically reparametrized semiempirical methods

Optimization approaches using several global and local algorithms (genetic algorithms, direct search, simplex and implicit filtering) in the search for a global minimum are applied to optimize auxiliary basis sets for quantum chemistry ab-initio calculations and to reparametrize semiempirical methods. We optimize auxiliary basis sets for RI-MP2 and RI-HF, by minimizing a suitable difference measure to the analogous calculations without the RI technique. It is shown that our methods of generating optimal auxiliary basis sets are more systematic and can be automatized more easily than the traditional approach. Hence, they can reasonably be expected to be faster and more reliable. At the same time, the quality of our basis sets is at least as good as that from the traditional approach. As an application, we present the first systematically optimized and complete set of mixed Poisson and density auxiliary basis sets for the atoms H, B, C, N, O and F, complementing the standard basis sets cc-pVXZ (X = D, T, Q and 5). As soon as efficient integral routines for this new basis function type become available, calculations with them will be much more efficient than with traditional basis sets. Similarly, these global and local optimization methods are also employed to reparametrize semiempirical methods for a difficult double proton transfer system. System-specific reparametrization of the well-known AM1, PM3 and PM5 methods is done by minimizing the error of the semiempirical calculations compared to ab-initio reference data at the MP2/aug-cc-pVDZ level. This is done at a small set of selected geometries, leading to one- and two-dimensional potential energy surfaces that are quantitatively in agreement with the ab-initio data over a much broader range of geometries. With this system-specific adaption, these reparametrized methods lead to results far superior to those obtainable with standard parameters. Nevertheless, the full speed advantage of the semiempirical approach is retained, offering the possibility to do direct dynamics studies with the potential energy surface calculated on the fly at ab-initio quality but at a fraction of the ab-initio cost. In both cases, our combination of genetic algorithm global search and Powell local search is the fastest and most robust choice for optimization, comparing with the other methods. Therefore, in these cases, a combination of global and local search is actually better than a purely local algorithm

Design and performance evaluation of indexing methods for dynamic attributes in mobile database management systems

Ankara : Department of Computer Engineering and Information Science and the Institute of Engineering and Science of Bilkent University, 1997.Thesis(Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 99-104.Tayeb, JamelM.S

Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of maximum total value that can be packed into the knapsacks without exceeding the capacities. We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing input. More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items. As the optimal and any approximate solution may change drastically, we maintain implicit solutions and support polylogarithmic time query operations that can return the computed solution value and the packing of any given item. While dynamic algorithms are well-studied in the context of graph problems, there is hardly any work on packing problems (and generally much less on non-graph problems). Motivated by the theoretical interest in knapsack problems and their practical relevance, our work bridges this gap