A new definition of program-size complexity is made. H(A;B=C;D) is defined to be the size in bits of the shortest self-delimiting program for calculating strings A and B if one is given a minimal-size selfdelimiting program for calculating strings C and D. This differs from previous definitions: (1) programs are required to be self-delimiting, i.e. no program is a prefix of another, and (2) instead of being given C and D directly, one is given a program for calculating them that is minimal in size. Unlike previous definitions, this one has precisely the formal 2 G. J. Chaitin properties of the entropy concept of information theory. For example, H(A;B) = H(A) + H(B=A) + O(1). Also, if a program of length k is assigned measure 2 \Gammak , then H(A) = \Gamma log 2 (the probability that the standard universal computer will calculate A) +O(1). Key Words and Phrases: computational complexity, entropy, information theory, instantaneous code, Kraft inequality, minimal program, probab...

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.

The technology underlying text search engines has advanced dramatically in the past decade. The development of a family of new index representations has led to a wide range of innovations in index storage, index construction, and query evaluation. While some of these developments have been consolidated in textbooks, many specific techniques are not widely known or the textbook descriptions are out of date. In this tutorial, we introduce the key techniques in the area, describing both a core implementation and how the core can be enhanced through a range of extensions. We conclude with a comprehensive bibliography of text indexing literature.

Query processing costs on large text databases are dominated by the need to retrieve and scan the inverted list of each query term. Here we show that query response time for conjunctive Boolean queries and for informal ranked queries can be dramatically reduced, at little cost in terms of storage, by the inclusion of an internal index in each inverted list. This method has been applied in a retrieval system for a collection of nearly two million short documents. Our experimental results show that the selfindexing strategy adds less than 20% to the size of the inverted file, but, for Boolean queries of 5--10 terms, can reduce processing time to under one fifth of the previous cost. Similarly, ranked queries of 40--50 terms can be evaluated in as little as 25% of the previous time, with little or no loss of retrieval effectiveness.

Ranking techniques are effective at finding answers in document collections but can be expensive to evaluate. We propose an evaluation technique that uses early recognition of which documents are likely to be highly ranked to reduce costs; for our test data, queries are evaluated in 2% of the memory of the standard implementation without degradation in retrieval effectiveness. cpu time and disk traffic can also be dramatically reduced by designing inverted indexes explicitly to support the technique. The principle of the index design is that inverted lists are sorted by decreasing within-document frequency rather than by document number, and this method experimentally reduces cpu time and disk traffic to around one third of the original requirement. We also show that frequency sorting can lead to a net reduction in index size, regardless of whether the index is compressed.

We survey the major techniques for information retrieval. In the rst part, weprovide an overview of the traditional ones (full text scanning, inversion, signature les and clustering). In the second part we discuss attempts to include semantic information (natural language processing, latent semantic indexing and neural networks).

This paper surveys a variety of data compression methods spanning almost forty years of research, from the work of Shannon, Fano and Huffman in the late 40's to a technique developed in 1986. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing effective data density. Data compression has important application in the areas of file storage and distributed systems. Concepts from information theory, as they relate to the goals and evaluation of data compression methods, are discussed briefly. A framework for evaluation and comparison of methods is constructed and applied to the algorithms presented. Comparisons of both theoretical and empirical natures are reported and possibilities for future research are suggested. INTRODUCTION Data compression is often referred to as coding, where coding is a very general term encompassing any special representation of data which satisfies a given need. Information theory is defined to be the study of eff...

We describe the implementation of a data compression scheme as an integral and transparent layer within a full-text...

Compression reduces both the size of indexes and the time needed to evaluate queries. In this paper, we revisit the compression of inverted lists of document postings that store the position and frequency of indexed terms, considering two approaches to improving retrieval efficiency: better implementation and better choice of integer compression schemes. First, we propose several simple optimisations to well-known integer compression schemes, and show experimentally that these lead to significant reductions in time. Second, we explore the impact of choice of compression scheme on retrieval efficiency. In experiments on large collections of data, we show two surprising results: use of simple byte-aligned codes halves the query evaluation time compared to the most compact Golomb-Rice bitwise compression schemes; and, even when an index fits entirely in memory, byte-aligned codes result in faster query evaluation than does an uncompressed index, emphasising that the cost of transferring data from memory to the CPU cache is less for an appropriately compressed index than for an uncompressed index. Moreover, byte-aligned schemes have only a modest space overhead: the most compact schemes result in indexes that are around 10 % of the size of the collection, while a byte-aligned scheme is around 13%. We conclude that fast byte-aligned codes should be used to store integers in inverted lists.

Abstract: Full-text database systems require an in-dex to allow fast access to documents based on their content. We propose an inverted file indexing scheme based on compression. This scheme allows users to retrieve documents using words occurring in the doc-uments, sequences of adjacent words, and statistical ranking techniques. The compression methods cho-sen ensure that the storage requirements are small and that dynamic update is straightforward. The only as-sumption that we make is that sufficient main memory is available to support an in-memory vocabulary; given this assumption, the method we describe requires at most one disc access per query term to identify an-swers to queries.