Full-text indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text length. This concept has evolved into self-indexes, which in addition contain enough information to reproduce any text portion, so they replace the text. The exciting possibility of an index that takes space close to that of the compressed text, replaces it, and in addition provides fast search over it, has triggered a wealth of activity and produced surprising results in a very short time, and radically changed the status of this area in less than five years. The most successful indexes nowadays are able to obtain almost optimal space and search time simultaneously. In this paper we present the main concepts underlying self-indexes. We explain the relationship between text entropy and regularities that show up in index structures and permit compressing them. Then we cover the most relevant self-indexes up to date, focusing on the essential aspects on how they exploit the text compressibility and how they solve efficiently various search problems. We aim at giving the theoretical background to understand and follow the developments in this area.

Abstract. Suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences. Practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to linear-time construction algorithms and more explicit structure. We narrow this gap between theory and practice with a simple linear-time construction algorithm for suffix arrays. The simplicity is demonstrated with a C++ implementation of 50 effective lines of code. The algorithm is called DC3, which stems from the central underlying concept of difference cover. This view leads to a generalized algorithm, DC, that allows a space-efficient implementation and, moreover, supports the choice of a space–time tradeoff. For any v ∈ [1, √ n], it runs in O(vn) time using O(n / √ v) space in addition to the input string and the suffix array. We also present variants of the algorithm for several parallel and hierarchical memory models of computation. The algorithms for BSP and EREW-PRAM models are asymptotically faster than all previous suffix tree or array construction algorithms.

Abstract. We present a linear time algorithm to sort all the suffixes of a string over a large alphabet of integers. The sorted order of suffixes of a string is also called suffix array, a data structure introduced by Manber and Myers that has numerous applications in pattern matching, string processing, and computational biology. Though the suffix tree of a string can be constructed in linear time and the sorted order of suffixes derived from it, a direct algorithm for suffix sorting is of great interest due to the space requirements of suffix trees. Our result improves upon the best known direct algorithm for suffix sorting, which takes O(n log n) time. We also show how to construct suffix trees in linear time from our suffix sorting result. Apart from being simple and applicable for alphabets not necessarily of fixed size, this method of constructing suffix trees is more space efficient. 1

Suffix trees and suffix arrays are the most prominent full-text indices, and their construction algorithms are well studied. It has been open for a long time whether these indicescan be constructed in both o(n log n) time and o(n log n)-bit working space, where n denotes the length of the text. Inthe literature, the fastest algorithm runs in O(n) time, whileit requires O(n log n)-bit working space. On the other hand,the most space-efficient algorithm requires O(n)-bit work-ing space while it runs in O(n log n) time. This paper breaks the long-standing time-and-space bar-rier under the unit-cost word RAM. We give an algorithm for constructing the suffix array which takes O(n) time and O(n)-bit working space, for texts with constant-size alpha-bets. Note that both the time and the space bounds are optimal. For constructing the suffix tree, our algorithm re-quires O(n logffl n) time and O(n)-bit working space forany 0! ffl! 1. Apart from that, our algorithm can alsobe adopted to build other existing full-text indices, such as

In 1990, Manber and Myers proposed suffix arrays as a space-saving alternative to suffix trees and described the first algorithms for suffix array construction and use. Since that time, and especially in the last few years, suffix array construction algorithms have proliferated in bewildering abundance. This survey paper attempts to provide simple high-level descriptions of these numerous algorithms that highlight both their distinctive features and their commonalities, while avoiding as much as possible the complexities of implementation details. New hybrid algorithms are also described. We provide comparisons of the algorithms ’ worst-case time complexity and use of additional space, together with results of recent experimental test runs on many of their implementations.

Cloning in software systems is known to create problems during software maintenance. Several techniques have been proposed to detect the same or similar code fragments in software, so-called simple clones. While the knowledge of simple clones is useful, detecting design-level similarities in software could ease maintenance even further, and also help us identify reuse opportunities. We observed that recurring patterns of simple clones – so-called structural clones- often indicate the presence of interesting design-level similarities. An example would be patterns of collaborating classes or components. Finding structural clones that signify potentially useful design information requires efficient techniques to analyze the bulk of simple clone data and making non-trivial inferences based on the abstracted information. In this paper, we describe a practical solution to the problem of

In this paper we consider the linear time algorithm of Kasai et al. [10] for the computation of the LCP array given the text and the su#x array. We show that this algorithm can be implemented without any auxiliary array in addition to the ones required for the input (the text and the su#x array) and the output (the LCP array). Thus, for a text of length n, we reduce the space occupancy of this algorithm from 13n bytes to 9n bytes.

We describe an algorithm that, for any v 2 [2; n], constructs the suffix array of a string of length n in O(vn + n log n) time using O(v + n= p v) space in addition to the input (the string) and the output (the suffix array). By setting v = log n, we obtain an O(n log n) time algorithm using O n= p

Suffix arrays are a simple and powerful data structure for text processing that can be used for full text indexes, data compression, and many other applications in particular in bioinformatics. However, so far it has looked prohibitive to build suffix arrays for huge inputs that do not fit into main memory. This paper presents design, analysis, implementation, and experimental evaluation of several new and improved algorithms for suffix array construction. The algorithms are asymptotically optimal in the worst case or on the average. Our implementation can construct suffix arrays for inputs of up to 4GBytes in hours on a low cost machine. As a tool of possible independent interest we present a systematic way to design, analyze, and implement pipelined algorithms.

We present a radically new indexing approach for approximate string matching. The scheme uses the metric properties of the edit distance and can be applied to any other metric between strings. We build a metric space where the sites are the nodes of the suffix tree of the text, and the approximate query is seen as a proximity query on that metric space. This permits us finding the R occurrences of a pattern of length m in a text of length n in average time O(m log n+m +R), using O(n log n) space and O(n log n) index construction time. This complexity improves by far over all other previous methods. We also show a simpler scheme needing O(n) space.