On the costs of optimal and near-optimal binary search trees

Summary We show that the cost of an optimal binary search tree can vary substantially, depending only on the left-to-right order imposed on the probabilities. We also prove that the costs of some common classes of near-optimal trees cannot be bounded above by the cost of an optimal tree plus a constant. This work was supported by the National Research Council of Canada, while the author was at the University of Waterloo     

On the information-based complexity of optimal reconstruction for nonlinear systems

The information-based complexity of optimal reconstruction problems for general nonlinear systems is studied. Both lower and upper bounds for the worst-case reconstruction-error functional are given. The existence of an optimal reconstruction algorithm which achieves the infimum of the reconstruction-error is established.     

On complications of search and realization in the state space of the optimal controllers

The solution which can be determined trivially in the operator space, in the state space was shown to be obtainable only after bulky computations. The resulting solution is just quasioptimal and difficult-to-realize. The problems presented by way of examples are often encountered in the practice of designing the control systems.     

Nearly optimal binary search trees

Summary We discuss two simple strategies for constructing binary search trees: Place the most frequently occurring name at the root of the tree, then proceed similary on the subtrees and choose the root so as to equalize the total weight of the left and right subtrees as much as possible, then proceed similarly on the subtres. While the former rule may yield extremely inefficient search trees, the latter rule always produces nearly optimal trees.     

The optimal binary search tree for Andersson's search algorithm

Andersson [1] presented a search algorithm for binary search trees that uses only two-way key comparisons by deferring equality comparisons until the leaves are reached. The use of a different search algorithm means that the optimal tree for the traditional search algorithm, which has been shown to be computable inO(n ²) time by Knuth [3], is not optimal with respect to the different search algorithm. This paper shows that the optimal binary search tree for Andersson's search algorithm can be computed inO(nlogn) time using existing algorithms for the special case of zero successful access frequencies, such as the Hu-Tucker algorithm [2].     

Algorithm for the optimal reconstruction of a digraph

Cybernetics and Systems Analysis -     

针式搜索在自催化反应解析中的应用

自催化反应一般比较复杂,其动力学模型往往未知。在其反应过程中获得的动力学一光谱数据矩阵可用迭代目标转换因子分析法(ITTFA)来解析。针式搜索被用来确定数据矩阵的化学秩及反应过程中所产生的中间体达到最大浓度的时间,并进一步构造ITTFA中的初始迭代矢量。应用此方法,一组含有两个中间体的自催化反应的模拟数据得到了成功的解析。硫酸介质中高锰酸钾氧化过氧化氢的反应属于自催化反应,在线测得的该反应的动力学-光谱数据用针式搜索-ITTFA方法进行了解析,确定反应过程中存在2个中间体,获得了反应体系中各组分的动力学谱。     

Temporal resolution using a breadth-first search algorithm

An approach to applying clausal resolution, a proof method well suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states, and temporal resolution between states. Not only has it been shown to be correct but as it consists of only one temporal resolution rule, it is particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, it is on this area that we focus. Detailed algorithms for abreadth‐first search approach to the application of this rule are presented. Correctness is shown and complexity given. Analysis of the behaviour of the algorithms is carried out and we explain why this approach is an improvement to others suggested. This revised version was published online in June 2006 with corrections to the Cover Date.     

Genetic search strategies in multicriterion optimal design

The present paper describes an implementation of genetic search methods in multicriterion optimal designs of structural systems with a mix of continuous, integer and discrete design variables. Two distinct strategies to simultaneously generate a family of Pareto optimal designs are presented in the paper. These strategies stem from a consideration of the natural analogue, wherein distinct species of life forms share the available resources of an environment for sustenance. The efficacy of these solution strategies are examined in the context of representative structural optimization problems with multiple objective criteria and with varying dimensionality as determined by the number of design variables and constraints.     

Discrete-variable optimal structural design using tabu search

Tabu search is a discrete-variable optimization algorithm with the ability to avoid entrapment by local optima and hence continue searching for a global optimum. In this paper tabu search is applied to the optimal structural design, in terms of weight minimization, of two standard (test) structural configurations; a 10-bar planar truss and a 25-bar space truss. The design variables are the cross-sectional areas of the bars, which take discrete values.An implementation of tabu search in a structural design context is presented which features-depth neighbourhoods and a search back-track facility. Investigations show that tabu search may readily cope with problem formulations that include buckling, gravity effects and design variables with realistic values. Furthermore, compared to previous research, superior (i.e. lower) minimum weights may be obtained.It is shown that tabu search is a technically viable technique for use in optimal structural design, although, for practical use, current (significant) execution times may inhibit its utilisation.     

Least adaptive optimal search with unreliable tests

We consider the basic problem of searching for an unknown m-bit number by asking the minimum possible number of yes–no questions, when up to a finite number e of the answers may be erroneous. In case the (i+1)th question is adaptively asked after receiving the answer to the ith question, the problem was posed by Ulam and Rényi and is strictly related to Berlekamp's theory of error correcting communication with noiseless feedback. Conversely, in the fully non-adaptive model when all questions are asked before knowing any answer, the problem amounts to finding a shortest e-error correcting code. Let q_e(m) be the smallest integer q satisfying Berlekamp’s bound . Then at least q_e(m) questions are necessary, in the adaptive, as well as in the non-adaptive model. In the fully adaptive case, optimal searching strategies using exactly q_e(m) questions always exist up to finitely many exceptional m's. At the opposite non-adaptive case, searching strategies with exactly q_e(m) questions—or equivalently, e-error correcting codes with 2^m codewords of length q_e(m)—are rather the exception, already for e=2, and are generally not known to exist for e>2. In this paper, for each e>1 and all sufficiently large m, we exhibit searching strategies that use a first batch of m non-adaptive questions and then, only depending on the answers to these m questions, a second batch of q_e(m)−m non-adaptive questions. These strategies are automatically optimal. Since even in the fully adaptive case, q_e(m)−1 questions do not suffice to find the unknown number, and q_e(m) questions generally do not suffice in the non-adaptive case, the results of our paper provide e fault tolerant searching strategies with minimum adaptiveness and minimum number of tests.     

High-speed reconstruction for ultra-low resolution faces

In this paper,a learning-based high-speed reconstruction system for ultra-low resolution faces is implemented using a software/hardware co-design paradigm.The hardware component working at 60 MHz contains a field programmable gate array,which is reconfigured to contain parallel processing units,and multiple memories to create parallel data.The hardware component effectively handles generating and sorting computationally intensive similarity metrics.This solves the processing speed problem in learning-based super-resolution reconstruction for ultra-low resolution faces.The system can reconstruct faces using 8 × 6,16 × 12,and 32 × 24 sized images,with 4 × 4,8 × 8,or 16 × 16 times magnification.The experimental results verify the effectiveness of our system in terms of both visual effect and low root mean square errors.The processing speed can be improved up to a maximum of 7900 times faster than a pure software implementation using C.     

Criterion for optimal image resolution using SIFT

Image processing is used to check products in many factories. If we use down-sampled images, we can reduce the calculation time and the image noise. However, the accuracy of the detection also becomes low. The purpose of this article is to estimate the optimal image resolution for detection while keeping the accuracy of detection high. To achieve our purpose, we adopt the scale invariant feature transform (SIFT) as the criterion of the optimal image resolution. Finally, we confirm that our proposed method is useful with a simulation.     

The optimal search for a Markovian target when the search path is constrained: the infinite-horizon case

A target moves among a finite number of cells according to a discrete-time homogeneous Markov chain. The searcher is subject to constraints on the search path, i.e., the cells available for search in the current epoch is a function of the cell searched in the previous epoch. The aim is to identify a search policy that maximizes the infinite-horizon total expected reward earned. We show the following structural results under the assumption that the target transition matrix is ergodic: 1) the optimal search policy is stationary; and 2) there exists /spl epsi/-optimal stationary policies which may be constructed by the standard value iteration algorithm in finite time. These results are obtained by showing that the dynamic programming operator associated with the search problem is an m-stage contraction mapping on a suitably defined space. An upper bound of m and the coefficient of contraction /spl alpha/ is given in terms of the transition matrix and other variables pertaining to the search problem. These bounds on m and /spl alpha/ may be used to derive bounds on suboptimal search polices constructed.     

Depth-first iterative-deepening: An optimal admissible tree search

The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iterative-deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches. The algorithm has been used successfully in chess programs, has been effectively combined with bi-directional search, and has been applied to best-first heuristic search as well. This heuristic depth-first iterative-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifteen Puzzle within practical resource limits.