A Bloom filter is a simple space-efficient randomized data structure for representing a set in order to support membership queries. Although Bloom filters allow false positives, for many applications the space savings outweigh this drawback when the probability of an error is sufficiently low. We introduce compressed Bloom filters, which improve performance when the Bloom filter is passed as a message, and its transmission size is a limiting factor. For example, Bloom filters have been suggested as a means for sharing Web cache information. In this setting, proxies do not share the exact contents of their caches, but instead periodically broadcast Bloom filters representing their cache. By using compressed Bloom filters, proxies can reduce the number of bits broadcast, the false positive rate, and/or the amount of computation per lookup. The cost is the processing time for compression and decompression, which can use simple arithmetic coding, and more memory use at the proxies, which utilize the larger uncompressed form of the Bloom filter.

In this paper, we consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by recently proposed random graph models for describing the Web.

Abstract—We show that the following simple compression problem is NP-hard: given a collection of documents, find the pair of Huffman dictionaries that minimizes the total compressed size of the collection, where the best dictionary from the pair is used to compress each document. We also show the NP-hardness of finding optimal multiple preset dictionaries for LZ’77-based compression schemes. Our reductions make use of the catalog segmentation problem, a natural partitioning problem. Our results justify heuristic attacks used in practice. Index Terms—Huffman coding, LZ’77, NP-completeness, preset dictionaries, two-stage compression.

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The frequency of words and other linguistic units plays a central role in all branches of corpus linguistics. Indeed, the use of frequency information distinguishes corpus-based methodology from other approaches to language. Thus, not surprisingly, the distribution of frequencies of words and combinations of

Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the virtues of this versatile data structure. In particular we show how to use wavelet trees to solve fundamental algorithmic problems such as range quantile queries, range next value queries, and range intersection queries. We explore several applications of these queries in Information Retrieval, in particular document retrieval in hierarchical and temporal documents, and in the representation of inverted lists.

We present a new variable-length encoding scheme for sequences of integers, Directly Addressable Codes (DACs), which enables direct access to any element of the encoded sequence without the need of any sampling method. Our proposal is a kind of implicit data structure that introduces synchronism in the encoded sequence without using asymptotically any extra space. We show some experiments demonstrating that the technique is not only simple, but also competitive in time and space with existing solutions in several applications, such as the representation of LCP arrays or high-order entropy-compressed sequences.