Fast Algorithms for Approximating Distances

In this paper we present efficient approximation algorithms for the distance selection problem. Our technique is based on the well-separated pair decomposition proposed in [8]. Received May 16, 1999; revised June 5, 2001.     

基于分割的字符串相似性查找算法

字符串相似性查找问题主要包括两方面,基于阈值的字符串相似性查找以及top-k字符串相似性查找。目前处理基于阈值的字符串相似性查找问题的算法多是基于过滤-验证框架的。基于该框架提出了PBsearch算法,算法在过滤阶段首次加入One-Off条件过滤掉大量的无效匹配,并在验证阶段提出了一种新的验证算法MultiThreshold算法,大大减少了计算编辑距离的次数。在top-k字符串相似性查找问题方面,提出了两种基于分割思想的算法,Pb-topk算法和PbCount-topk算法。其中,Pb-topk算法采用差值递增的策略,减少了需处理的字符串数目;PbCount-topk算法采用匹配数目划分的策略,进一步缩小了候选集的规模。最后,通过在3个真实数据集上的实验结果,验证了提出算法的高效性。     

Approximating Tree Edit Distance through String Edit Distance

We present an algorithm to approximate edit distance between two ordered and rooted trees of bounded degree. In this algorithm, each input tree is transformed into a string by computing the Euler string, where labels of some edges in the input trees are modified so that structures of small subtrees are reflected to the labels. We show that the edit distance between trees is at least 1/6 and at most O(n ^3/4) of the edit distance between the transformed strings, where n is the maximum size of two input trees and we assume unit cost edit operations for both trees and strings. The algorithm works in O(n ²) time since computation of edit distance and reconstruction of tree mapping from string alignment takes O(n ²) time though transformation itself can be done in O(n) time.     

Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications

This paper proposes accurate and robust algorithms for approximating variable order fractional derivatives of arbitrary order. The proposed schemes are based on finite difference approximations. We compare the performance of algorithms by introducing a new formulation of experimental convergence order. Two initial value problems are considered and solved by means of the proposed methods. Numerical results are provided justifying the usefulness of the proposed methods.     

A Comparison of Approximate String Matching Algorithms

Experimental comparisons of the running time of approximate string matching algorithms for the k differences problem are presented. Given a pattern string, a text string, and an integer k, the task is to find all approximate occurrences of the pattern in the text with at most k differences (insertions, deletions, changes). We consider seven algorithms based on different approaches including dynamic programming, Boyer–Moore string matching, suffix automata, and the distribution of characters. It turns out that none of the algorithms is the best for all values of the problem parameters, and the speed differences between the methods can be considerable.     

几种字符串匹配算法的分析和比较

字符串匹配技术在许多领域里被广泛应用。分析了BF、KMP、BM算法以及一些重要的改进算法,并对其性能进行了测试,为不同的应用领域采用适当的算法提供了思路。     

On-Line Approximate String Searching Algorithms: Survey and Experimental Results

The problem of approximate string searching comprises two classes of problems: string searching with k mismatches and string searching with k differences. In this paper we present a short survey and experimental results for well known sequential approximate string searching algorithms. We consider algorithms based on different approaches including dynamic programming, deterministic finite automata, filtering, counting and bit parallelism. We compare these algorithms in terms of running time against pattern length and for several values of k for four different kinds of text: binary alphabet, alphabet of size 8, English alphabet and DNA alphabet. Finally, we compare the experimental results of the algorithms with their theoretical complexities.     

异构机群系统上基于多轮分配方式的近似串匹配并行算法

在给定正文串分配轮数的前提下,考虑处理机节点具有不同计算速度、不同通信能力的情形,根据从处理机是否允许重叠执行计算和通信操作,提出异构机群计算环境下的最优正文串多轮分配策略;同时提出一种周期性的正文串多轮分配策略并给出了相应的正文串多轮分配的闭合解,此策略可以求出最优的分配轮数.实验结果表明,正文串多轮分配策略比正文串单轮分配策略大大缩短了近似串匹配并行处理的时间,并且在正文串多轮分配策略中,当近似串匹配应用的规模较小时,分配轮数比参与近似串匹配并行处理的从处理机数更能影响近似串匹配并行处理的完成时间,反之,从处理机数对近似串匹配并行处理的完成时间影响更大.     

Approximating traces

In order to give a semantics to concurrent processes we need a model having some good mathematical properties. To this end we generalize (infinite) Mazurkiewicz traces by adding some alphabetical information concerning the possible continuations of a process. This allows to define an approximation order compatible with the composition. We obtain a prime algebraic and coherently complete domain where the compact elements are exactly the finite approximations of processes. The composition is shown to be monotone and -continuous. We define a suitable metric which induces the Lawson topology and which yields a compact metric space being therefore complete. The finite approximations of processes form a dense and open subset and the composition is (uniformly) continuous. A preliminary version of this work appeared in [7]. Received: 2 July 1996 / 27 October 1997     

Automated String Constraints Solving for Programs Containing String Manipulation Functions

The ability to solve various constraints is a principal factor of automatic constraint solvers. Most object-oriented languages treat a character string as a primitive data type which is manipulated by string library functions. Most constraint solvers have limitations on their input constraints, such as strong restrictions on the expressiveness of constraints or lack of the ability to solve hybrid constraints. These limitations hinder applying automated constraint solvers on program analysis techniques for programs containing strings and string manipulation functions. We propose an approach to automatically solve program constraints involving strings and string manipulation functions. Based on the character array model, we design a constraint language which contains primitive operations to precisely describe the constraints of commonly used string manipulation functions. The translated string constraints together with numeric constraints are then solved by a two-phase test generation procedure: firstly, a partial solution is obtained to satisfy the arithmetic constraints of the position variables, and the solution is utilized to simplify the string constraints into pure character array constraints; secondly, the pure array constraints are solved by an off-the-shelf array-specific theory based constraint solver. We integrate the approach into an automated testing tool to support the generation of string test cases, and then perform experiments. The results of the experiments prove that the integration of the proposed approach promotes the testing coverage of the existing testing tool, and the integrated tool has an advantage of handling specific string manipulation functions compared with an existing string solver.     

Approximating performance measures for public services

This paper deals with estimating performance measures, such as average response time for spatially distributed networks. Demands are generated stochastically at the nodes and the service units are stationed at service centers when available. Whenever a call arrives, a service unit will travel to the call's location. When there are no available servers, the call will enter an infinite capacity queue at that node. The service units will travel from node to node serving the calls and return to the service center only when there are no more calls waiting. In most cases, exact models are too complicated to analyze. This paper presents approximations which are tested using simulation and found to give good results.     

Sublinear merging and natural mergesort

The complexity of merging two sorted sequences into one is linear in the worst case as well as in the average case. There are, however, instances for which a sublinear number of comparisons is sufficient. We consider the problem of measuring and exploiting such instance easiness. The merging algorithm presented, Adaptmerge, is shown to adapt optimally to different kinds of measures of instance easiness. In the sorting problem the concept of instance easiness has received a lot of attention, and it is interpreted by a measure of presortedness. We apply Adaptmerge in the already adaptive sorting algorithm Natural Mergesort. The resulting algorithm, Adaptive Mergesort, optimally adapts to several, known and new, measures of presortedness. We also prove some interesting results concerning the relation between measures of presortedness proposed in the literature.     

Sublinear Fully Distributed Partition with Applications

We present new efficient deterministic and randomized distributed algorithms for decomposing a graph with n nodes into a disjoint set of connected clusters with radius at most k−1 and having O(n ^1+1/k ) intercluster edges. We show how to implement our algorithms in the distributed CONGEST\mathcal{CONGEST} model of computation, i.e., limited message size, which improves the time complexity of previous algorithms (Moran and Snir in Theor. Comput. Sci. 243(1–2):217–241, 2000; Awerbuch in J. ACM 32:804–823, 1985; Peleg in Distributed Computing: A Locality-Sensitive Approach, 2000) from O(n) to O(n ^1−1/k ). We apply our algorithms for constructing low stretch graph spanners and network synchronizers in sublinear deterministic time in the CONGEST\mathcal{CONGEST} model.     

Approximating the crowd

The problem of “approximating the crowd” is that of estimating the crowd’s majority opinion by querying only a subset of it. Algorithms that approximate the crowd can intelligently stretch a limited budget for a crowdsourcing task. We present an algorithm, “CrowdSense,” that works in an online fashion where items come one at a time. CrowdSense dynamically samples subsets of the crowd based on an exploration/exploitation criterion. The algorithm produces a weighted combination of the subset’s votes that approximates the crowd’s opinion. We then introduce two variations of CrowdSense that make various distributional approximations to handle distinct crowd characteristics. In particular, the first algorithm makes a statistical independence approximation of the labelers for large crowds, whereas the second algorithm finds a lower bound on how often the current subcrowd agrees with the crowd’s majority vote. Our experiments on CrowdSense and several baselines demonstrate that we can reliably approximate the entire crowd’s vote by collecting opinions from a representative subset of the crowd.     

Self-Assembling Rulers for Approximating Generalized Sierpinski Carpets

Discrete self-similar fractals have been used as test cases for self-assembly, both in the laboratory and in mathematical models, ever since Winfree exhibited a tile assembly system in which the Sierpinski triangle self-assembles. For strict self-assembly, where tiles are not allowed to be placed outside the target structure, it is an open question whether any self-similar fractal can self-assemble. This has motivated the development of techniques to approximate fractals with strict self-assembly. Ideally, such an approximation would produce a structure with the same fractal dimension as the intended fractal, but with specially labeled tiles at positions corresponding to points in the fractal. We show that the Sierpinski carpet, along with an infinite class of related fractals, can approximately self-assemble in this manner. Our construction takes a set of parameters specifying a target fractal and creates a tile assembly system in which the fractal approximately self-assembles. This construction introduces rulers and readers to control the self-assembly of a fractal structure without distorting it. To verify the fractal dimension of the resulting assemblies, we prove a result on the dimension of sets embedded into discrete fractals. We also give a conjecture on the limitations of approximating self-similar fractals.     

String sorting technique for microcomputers

This paper reports the development of a sorting algorithm, called a ‘pocket sort.’ It is primarily directed to sorting of character data. The algorithm is strictly of order O(n); sorting time is directly proportional to the number of data elements to be sorted. Further, through the use of pointer - linked list data structures, no internal movement of the records containing the sort field is required. The algorithm has been implemented in Turbo Pascal. Data are presented comparing this pocket sort to other sorting techniques.