The charter of SRC is to advance both the state of knowledge and the state of the art in computer systems. From our establishment in 1984, we have performed basic and applied research to support Digital’s business objectives. Our current work includes exploring distributed personal computing on multiple platforms, networking, programming technology, system modelling and management techniques, and selected applications. Our strategy is to test the technical and practical value of our ideas by building hardware and software prototypes and using them as daily tools. Interesting systems are too complex to be evaluated solely in the abstract; extended use allows us to investigate their properties in depth. This experience is useful in the short term in refining our designs, and invaluable in the long term in advancing our knowledge. Most of the major advances in information systems have come through this strategy, including personal computing, distributed systems, and the Internet. We also perform complementary work of a more mathematical flavor. Some of it is in established fields of theoretical computer science, such as the analysis of algorithms, computational geometry, and logics of programming. Other work explores new ground motivated by problems that arise in our systems research. We have a strong commitment to communicating our results; exposing and testing our ideas in the research and development communities leads to improved understanding. Our research report series supplements publication in professional journals and conferences. We seek users for our prototype systems among those with whom we have common interests, and we encourage collaboration with university researchers.

We present a novel implementation of compressed suffix arrays exhibiting new tradeoffs between search time and space occupancy for a given text (or sequence) of n symbols over an alphabet Σ, where each symbol is encoded by lg |Σ | bits. We show that compressed suffix arrays use just nHh + O(n lg lg n / lg |Σ | n) bits, while retaining full text indexing functionalities, such as searching any pattern sequence of length m in O(m lg |Σ | + polylog(n)) time. The term Hh ≤ lg |Σ | denotes the hth-order empirical entropy of the text, which means that our index is nearly optimal in space apart from lower-order terms, achieving asymptotically the empirical entropy of the text (with a multiplicative constant 1). If the text is highly compressible so that Hh = o(1) and the alphabet size is small, we obtain a text index with o(m) search time that requires only o(n) bits. Further results and tradeoffs are reported in the paper. 1

In this paper we address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space reduction is achieved at no significant slowdown in the query performance. More precisely, its space occupancy is optimal in an information-content sense because a text T [1, u] is stored using O(H k (T )) + o(1) bits per input symbol in the worst case, where H k (T ) is the kth order empirical entropy of T (the bound holds for any fixed k). Given an arbitrary string P [1; p], the opportunistic data structure allows to search for the occ occurrences of P in T in O(p + occ log u) time (for any fixed > 0). If data are uncompressible we achieve the best space bound currently known [12]; on compressible data our solution improves the succinct suffix array of [12] and the classical suffix tree and suffix array data structures either in space or in query time or both.

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.

We present theoretical algorithms for sorting and searching multikey data, and derive from them practical C implementations for applications in which keys are character strings. The sorting algorithm blends Quicksort and radix sort; it is competitive with the best known C sort codes. The searching algorithm blends tries and binary search trees; it is faster than hashing and other commonly used search methods. The basic ideas behind the algorithms date back at least to the 1960s, but their practical utility has been overlooked. We also present extensions to more complex string problems, such as partial-match searching. 1. Introduction Section 2 briefly reviews Hoare's [9] Quicksort and binary search trees. We emphasize a well-known isomorphism relating the two, and summarize other basic facts. The multikey algorithms and data structures are presented in Section 3. Multikey Quicksort orders a set of n vectors with k components each. Like regular Quicksort, it partitions its input into...

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.

We introduce a new text-indexing data structure, the String B-Tree, that can be seen as a link between some traditional external-memory and string-matching data structures. In a short phrase, it is a combination of B-trees and Patricia tries for internal-node indices that is made more effective by adding extra pointers to speed up search and update operations. Consequently, the String B-Tree overcomes the theoretical limitations of inverted files, B-trees, prefix B-trees, suffix arrays, compacted tries and suffix trees. String B-trees have the same worst-case performance as B-trees but they manage unbounded-length strings and perform much more powerful search operations such as the ones supported by suffix trees. String B-trees are also effective in main memory (RAM model) because they improve the online suffix tree search on a dynamic set of strings. They also can be successfully applied to database indexing and software duplication.

We show that suffix trees store various kinds of redundant information. We exploit these redundancies to obtain more space efficient representations. The most space efficient of our representations requires 20 bytes per input character in the worst case, and 10.1 bytes per input character on average for a collection of 42 files of different type. This is an advantage of more than 8 bytes per input character over previous work. Our representations can be constructed without extra space, and as fast as previous representations. The asymptotic running times of suffix tree applications are retained. Copyright © 1999 John Wiley & Sons, Ltd. KEY WORDS: data structures; suffix trees; implementation techniques; space reduction

We offer an overview of current Web search engine design. After introducing a generic search engine architecture, we examine each engine component in turn. We cover crawling, local Web page storage, indexing, and the use of link analysis for boosting search performance. The most common design and implementation techniques for each of these components are presented. For this presentation we draw from the literature and from our own experimental search engine testbed. Emphasis is on introducing the fundamental concepts and the results of several performance analyses we conducted to compare different designs.

Abstract. Given a sequence S = s1s2... sn of integers smaller than r = O(polylog(n)), we show how S can be represented using nH0(S) + o(n) bits, so that we can know any sq, as well as answer rank and select queries on S, in constant time. H0(S) is the zero-order empirical entropy of S and nH0(S) provides an Information Theoretic lower bound to the bit storage of any sequence S via a fixed encoding of its symbols. This extends previous results on binary sequences, and improves previous results on general sequences where those queries are answered in O(log r) time. For larger r, we can still represent S in nH0(S) + o(n log r) bits and answer queries in O(log r / log log n) time. Another contribution of this paper is to show how to combine our compressed representation of integer sequences with an existing compression boosting technique to design compressed full-text indexes that scale well with the size of the input alphabet Σ. Namely, we design a variant of the FM-index that indexes a string T [1, n] within nHk(T) + o(n) bits of storage, where Hk(T) is the k-th order empirical entropy of T. This space bound holds simultaneously for all k ≤ α log |Σ | n, constant 0 < α < 1, and |Σ | = O(polylog(n)). This index counts the occurrences of an arbitrary pattern P [1, p] as a substring of T in O(p) time; it locates each pattern occurrence in O(log 1+ε n) time, for any constant 0 < ε < 1; and it reports a text substring of length ℓ in O(ℓ + log 1+ε n) time.