LCS approximation via embedding into locally non-repetitive strings

A classical measure of similarity between strings is the length of the longest common subsequence (LCS) between the two given strings. The search for efficient algorithms for finding the LCS has been going on for more than three decades. To date, all known algorithms may take quadratic time (shaved by logarithmic factors) to find large LCS. In this paper, the problem of approximating LCS is studied, while focusing on the hard inputs for this problem, namely, approximating LCS of near-linear size in strings over a relatively large alphabet (of size at least n^? for some constant ?>0, where n is the length of the string). We show that, any given string over a relatively large alphabet can be embedded into a locally non-repetitive string. This embedding has a negligible additive distortion for strings that are not too dissimilar in terms of the edit distance. We also show that LCS can be efficiently approximated in locally-non-repetitive strings. Our new method (the embedding together with the approximation algorithm) gives a strictly sub-quadratic time algorithm (i.e., of complexity O(n^2-?) for some constant ?) which can find common subsequences of linear (and near linear) size that cannot be detected efficiently by the existing tools.     

双向过滤的字符串相似连接验证方法

字符串相似连接是指在字符串集合中找出相似的字符串对,是许多应用的关键操作,寻找高效的字符串相似连接算法已成为研究热点。基于划分的过滤-验证方法（Pass-Join）与其他方法相比具有较高的效率。它按照字符串长度递增的顺序访问字符串集合,通过查找一个字符串的划分块是否存在于另一个字符串中,快速筛选出可能相似的字符串对（候选集）,然后利用编辑距离进行相似性验证。研究发现,按照字符串长度递减的顺序进行过滤（长度递减过滤）的效果优于按照长度递增的顺序过滤（长度递增过滤）的效果,基于此,提出双向过滤-验证机制：在过滤阶段对长度递减过滤的结果再进行一次长度递增过滤,进一步减小候选集大小;在验证阶段利用双向过滤产生的两对划分块和其匹配子串分隔字符串对,从而减小需要验证的字符串的长度,加速验证过程。实验证明,双向过滤-验证算法在真实数据集上优于原算法。     

Engineering scalable, cache and space efficient tries for strings

Storing and retrieving strings in main memory is a fundamental problem in computer science. The efficiency of string data structures used for this task is of paramount importance for applications such as in-memory databases, text-based search engines and dictionaries. The burst trie is a leading choice for such tasks, as it can provide fast sorted access to strings. The burst trie, however, uses linked lists as substructures which can result in poor use of CPU cache and main memory. Previous research addressed this issue by replacing linked lists with dynamic arrays forming a cache-conscious array burst trie. Though faster, this variant can incur high instruction costs which can hinder its efficiency. Thus, engineering a fast, compact, and scalable trie for strings remains an open problem. In this paper, we introduce a novel and practical solution that carefully combines a trie with a hash table, creating a variant of burst trie called HAT-trie. We provide a thorough experimental analysis which demonstrates that for large set of strings and on alternative computing architectures, the HAT-trie—and two novel variants engineered to achieve further space-efficiency—is currently the leading in-memory trie-based data structure offering rapid, compact, and scalable storage and retrieval of variable-length strings.     

Meta similarity

To see if two given strings are matched, various string similarity metrics have been employed and these string similarities can be categorized into three classes: (a) Edit-distance-based similarities, (b) Token-based similarities, and (c) Hybrid similarities. In essence, since different types of string similarities have different pros and cons in measuring the similarity between two strings, string similarity metrics in each class are likely to work well for particular data sets. Toward this problem, we propose a novel Meta Similarity that both (i) outperforms the existing similarity metrics and (ii) is the least affected by a variety of data sets. Our claim is empirically validated through extensive experimental tests—our proposal shows an improvement to the largest 20% average recall, compared to the best case of the existing similarity metrics and our method is the most stable, showing from 0.95 to 1.0 average recall range in all the data sets.     

A hash trie filter method for approximate string matching in genomic databases

In genomic databases, approximate string matching with k errors is often applied when searching genomic sequences, where k errors can be caused by substitution, insertion, or deletion operations. In this paper, we propose a new method, the hash trie filter, to efficiently support approximate string matching in genomic databases. First, we build a hash trie for indexing the genomic sequence stored in a database in advance. Then, we utilize an efficient technique to find the ordered subpatterns in the sequence, which could reduce the number of candidates by pruning some unreasonable matching positions. Moreover, our method will dynamically decide the number of ordered matching grams, resulting in the increase of precision. The simulation results show that the hash trie filter outperforms the well-known (k+s) q-samples filter in terms of the response time, the number of verified candidates, and the precision, under different lengths of the query patterns and different error levels.     

Iconic indexing by 2-d strings

In this paper, we describe a new way of representing a symbolic picture by a two-dimensional string. A picture query can also be specified as a 2-D string. The problem of pictorial information retrieval then becomes a problem of 2-D subsequence matching. We present algorithms for encoding a symbolic picture into its 2-D string representation, reconstructing a picture from its 2-D string representation, and matching a 2-D string with another 2-D string. We also prove the necessary and sufficient conditions to characterize ambiguous pictures for reduced 2-D strings as well as normal 2-D strings. This approach thus allows an efficient and natural way to construct iconic indexes for pictures.     

Discovering Frequent Closed Partial Orders from Strings

Mining knowledge about ordering from sequence data is an important problem with many applications, such as bioinformatics, Web mining, network management, and intrusion detection. For example, if many customers follow a partial order in their purchases of a series of products, the partial order can be used to predict other related customers' future purchases and develop marketing campaigns. Moreover, some biological sequences (e.g., microarray data) can be clustered based on the partial orders shared by the sequences. Given a set of items, a total order of a subset of items can be represented as a string. A string database is a multiset of strings. In this paper, we identify a novel problem of mining frequent closed partial orders from strings. Frequent closed partial orders capture the nonredundant and interesting ordering information from string databases. Importantly, mining frequent closed partial orders can discover meaningful knowledge that cannot be disclosed by previous data mining techniques. However, the problem of mining frequent closed partial orders is challenging. To tackle the problem, we develop Frecpo (for frequent closed partial order), a practically efficient algorithm for mining the complete set of frequent closed partial orders from large string databases. Several interesting pruning techniques are devised to speed up the search. We report an extensive performance study on both real data sets and synthetic data sets to illustrate the effectiveness and the efficiency of our approach     

SEPIA: estimating selectivities of approximate string predicates in large Databases

Many database applications have the emerging need to support approximate queries that ask for strings that are similar to a given string, such as “name similar to smith” and “telephone number similar to 412-0964”. Query optimization needs the selectivity of such an approximate predicate, i.e., the fraction of records in the database that satisfy the condition. In this paper, we study the problem of estimating selectivities of approximate string predicates. We develop a novel technique, called Sepia, to solve the problem. Given a bag of strings, our technique groups the strings into clusters, builds a histogram structure for each cluster, and constructs a global histogram. It is based on the following intuition: given a query string q, a preselected string p in a cluster, and a string s in the cluster, based on the proximity between q and p, and the proximity between p and s, we can obtain a probability distribution from a global histogram about the similarity between q and s. We give a full specification of the technique using the edit distance metric. We study challenges in adopting this technique, including how to construct the histogram structures, how to use them to do selectivity estimation, and how to alleviate the effect of non-uniform errors in the estimation. We discuss how to extend the techniques to other similarity functions. Our extensive experiments on real data sets show that this technique can accurately estimate selectivities of approximate string predicates. A short version of this article appeared as [21] in the proceedings of the 31st International Conference on Very Large Data Bases (VLDB), August 30 – September 2, 2005, Trondheim, Norway. The source code of our algorithms is available at .     

Average-Case Analysis of Approximate Trie Search

For the exact search of a pattern of length m in a database of n strings the trie data structure allows an optimal lookup time of O(m). If mismatches are allowed between the pattern and the database strings, no such structure with reasonable size is known. Some work can be saved using a trie and running times superior to the comparison with every string in the database can be achieved. We investigate a comparison-based model where matches and mismatches are defined between pairs of characters. When comparing two characters, let q be the probability of an error. Between any two strings we bound the number of errors by d, which we consider a function of n. We study the average-case complexity of the number of comparisons for searching in a trie in dependence of the parameters q and d. Our analysis yields the asymptotic behavior for memoryless sources with uniform probabilities. It turns out that there is a jump in the average-case complexity at certain thresholds for q and d. Our results can be applied for any comparison-based error model, for instance, Hamming distance, don't cares, or geometric character distances.     

Similarity query support in big data management systems

Similarity query processing is becoming increasingly important in many applications such as data cleaning, record linkage, Web search, and document analytics. In this paper we study how to provide end-to-end similarity query support natively in a parallel database system. We discuss how to express a similarity predicate in its query language, how to build indexes, how to answer similarity queries (selections and joins) efficiently in the runtime engine, possibly using indexes, and how to optimize similarity queries. One particular challenge is how to incorporate existing similarity join algorithms, which often require a series of steps to achieve a high efficiency, including collecting token frequencies, finding matching record id pairs, and reassembling result records based on id pairs. We present a novel approach that uses existing runtime operators to implement such complex join algorithms without reinventing the wheel; doing so positions the system to automatically benefit from future improvements to those operators. The approach includes a technique to transform a similarity join plan into an efficient operator-based physical plan during query optimization by using a template expressed largely in the system’s user-level query language; this technique greatly simplifies the specification of such a transformation rule. We use Apache AsterixDB, a parallel Big Data management system, to illustrate and validate our techniques. We conduct an experimental study using several large, real datasets on a parallel computing cluster to assess the similarity query support. We also include experiments involving three other parallel systems and report the efficacy and performance results.