Results 1  10
of
27
Succinct indexes for strings, binary relations, and multilabeled trees
 IN: PROC. SODA
, 2007
"... We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the informationtheoretic lower bound on the space required to encode the given data, and support an extended set of ope ..."
Abstract

Cited by 41 (12 self)
 Add to MetaCart
We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the informationtheoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. The main advantage of succinct indexes as opposed to succinct (integrated data/index) encodings is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this paper, we present succinct indexes for various data types, namely strings, binary relations and multilabeled trees. Given the support for the interface of the ADTs of these data types, we can support various useful operations efficiently by constructing succinct indexes for them. When the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we design a succinct encoding that represents a string of length n over an alphabet of size σ using nHk(S)+lgσ·o(n)+O ( nlgσ lglglgσ) bits to support access/rank/select operations in o((lglgσ)1+ɛ) time, for any fixed constant ɛ> 0. We also design a succinct text index using nH0(S)+O ( nlgσ) bits that lglgσ
Compressed representations of permutations, and applications
 SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
"... We explore various techniques to compress a permutation π over n integers, taking advantage of ordered subsequences in π, while supporting its application π(i) and the application of its inverse π −1 (i) in small time. Our compression schemes yield several interesting byproducts, in many cases mat ..."
Abstract

Cited by 20 (12 self)
 Add to MetaCart
We explore various techniques to compress a permutation π over n integers, taking advantage of ordered subsequences in π, while supporting its application π(i) and the application of its inverse π −1 (i) in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications π k (i) of it, of integer functions, and of inverted lists and suffix arrays.
Alphabet Partitioning for Compressed Rank/Select and Applications
"... Abstract. We present a data structure that stores a string s[1..n] over the alphabet [1..σ] in nH0(s) + o(n)(H0(s)+1) bits, where H0(s) is the zeroorder entropy of s. This data structure supports the queries access and rank in time O (lg lg σ), and the select query in constant time. This result imp ..."
Abstract

Cited by 18 (13 self)
 Add to MetaCart
(Show Context)
Abstract. We present a data structure that stores a string s[1..n] over the alphabet [1..σ] in nH0(s) + o(n)(H0(s)+1) bits, where H0(s) is the zeroorder entropy of s. This data structure supports the queries access and rank in time O (lg lg σ), and the select query in constant time. This result improves on previously known data structures using nH0(s) + o(n lg σ) bits, where on highly compressible instances the redundancy o(n lg σ) cease to be negligible compared to the nH0(s) bits that encode the data. The technique is based on combining previous results through an ingenious partitioning of the alphabet, and practical enough to be implementable. It applies not only to strings, but also to several other compact data structures. For example, we achieve (i) faster search times and lower redundancy for the smallest existing fulltext selfindex; (ii) compressed permutations π with times for π() and π −1 () improved to loglogarithmic; and (iii) the first compressed representation of dynamic collections of disjoint sets. 1
A Fast and Compact Web Graph Representation
"... Compressed graphs representation has become an attractive research topic because of its applications in the manipulation of huge Web graphs in main memory. By far the best current result is the technique by Boldi and Vigna, which takes advantage of several particular properties of Web graphs. In t ..."
Abstract

Cited by 17 (12 self)
 Add to MetaCart
(Show Context)
Compressed graphs representation has become an attractive research topic because of its applications in the manipulation of huge Web graphs in main memory. By far the best current result is the technique by Boldi and Vigna, which takes advantage of several particular properties of Web graphs. In this paper we show that the same properties can be exploited with a different and elegant technique, built on RePair compression, which achieves about the same space but much faster navigation of the graph. Moreover, the technique has the potential of adapting well to secondary memory. In addition, we introduce an approximate RePair version that works efficiently with limited main memory.
Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing
"... We present a succinct representation of a set of n points on an n × n grid using n lg n + o(nlg n) bits 3 to support orthogonal range counting in O(lg n / lg lg n) time, and range reporting in O(k lg n/lg lg n) time, where k is the size of the output. This achieves an improvement on query time by ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
We present a succinct representation of a set of n points on an n × n grid using n lg n + o(nlg n) bits 3 to support orthogonal range counting in O(lg n / lg lg n) time, and range reporting in O(k lg n/lg lg n) time, where k is the size of the output. This achieves an improvement on query time by a factor of lg lg n upon the previous result of Mäkinen and Navarro [15], while using essentially the informationtheoretic minimum space. Our data structure not only can be used as a key component in solutions to the general orthogonal range search problem to save storage cost, but also has applications in text indexing. In particular, we apply it to improve two previous spaceefficient text indexes that support substring search [7] and positionrestricted substring search [15]. We also use it to extend previous results on succinct representations of sequences of small integers, and to design succinct data structures supporting certain types of orthogonal range query in the plane.
Improved dynamic rankselect entropybound structures
 in Proc. of the Latin American Theoretical Informatics (LATIN
"... Abstract. Operations rank and select over a sequence of symbols have many applications to the design of succinct and compressed data structures to manage text collections, structured text, binary relations, trees, graphs, and so on. We are interested in the case where the collections can be updated ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
Abstract. Operations rank and select over a sequence of symbols have many applications to the design of succinct and compressed data structures to manage text collections, structured text, binary relations, trees, graphs, and so on. We are interested in the case where the collections can be updated via insertions and deletions of symbols. Two current solutions stand out as the best in the tradeoff of space versus time (considering all the operations). One by Mäkinen and Navarro achieves compressed space (i.e., nH0 + o(n log σ) bits) and O(log nlog σ) worstcase time for all the operations, where n is the sequence length, σ is the alphabet size, and H0 is the zeroorder entropy of the sequence. The other log σ log log n solution, by Lee and Park, achieves O(log n(1 +)) amortized time and uncompressed space, i.e. nlog σ +O(n)+o(nlog σ) bits. In this paper we show that the best of both worlds can be achieved. We log σ combine the solutions to obtain nH0+o(nlog σ) bits of space and O(log n(1+)) worstcase time log log n for all the operations. Apart from the best current solution, we obtain some byproducts that might be
Compact RichFunctional Binary Relation Representations
"... Abstract. Binary relations are an important abstraction arising in a number of data representation problems. Each existing data structure specializes in the few basic operations required by one single application, and takes only limited advantage of the inherent redundancy of binary relations. We sh ..."
Abstract

Cited by 12 (7 self)
 Add to MetaCart
(Show Context)
Abstract. Binary relations are an important abstraction arising in a number of data representation problems. Each existing data structure specializes in the few basic operations required by one single application, and takes only limited advantage of the inherent redundancy of binary relations. We show how to support more general operations efficiently, while taking better advantage of some forms of redundancy in practical instances. As a basis for a more general discussion on binary relation data structures, we list the operations of potential interest for practical applications, and give reductions between operations. We identify a set of operations that yield the support of all others. As a first contribution to the discussion, we present two data structures for binary relations, each of which achieves a distinct tradeoff between the space used to store and index the relation, the set of operations supported in sublinear time, and the time in which those operations are supported. The experimental performance of our data structures shows that they not only offer good time complexities to carry out many operations, but also take advantage of regularities that arise in practical instances in order to reduce space usage. 1
Succinct Representation of Labeled Graphs
 ALGORITHMICA
, 2010
"... In many applications, the properties of an object being modeled are stored as labels on vertices or edges of a graph. In this paper, we consider succinct representation of labeled graphs. Our main results are the succinct representations of labeled and multilabeled graphs (we consider planar triang ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
In many applications, the properties of an object being modeled are stored as labels on vertices or edges of a graph. In this paper, we consider succinct representation of labeled graphs. Our main results are the succinct representations of labeled and multilabeled graphs (we consider planar triangulations, planar graphs and kpage graphs) to support various label queries efficiently. The additional space cost to store the labels is essentially the informationtheoretic minimum. As far as we know, our representations are the first succinct representations of labeled graphs. We also have two preliminary results to achieve the main contribution. First, we design a succinct representation of unlabeled planar triangulations to support the rank/select of edges in ccw (counter clockwise) order in addition to the other operations supported in previous work. Second, we design a succinct representation for a kpage
Extended Compact Web Graph Representations
"... Abstract. Many relevant Web mining tasks translate into classical algorithms on the Web graph. Compact Web graph representations allow running these tasks on larger graphs within main memory. These representations at least provide fast navigation (to the neighbors of a node), yet more sophisticated ..."
Abstract

Cited by 9 (6 self)
 Add to MetaCart
(Show Context)
Abstract. Many relevant Web mining tasks translate into classical algorithms on the Web graph. Compact Web graph representations allow running these tasks on larger graphs within main memory. These representations at least provide fast navigation (to the neighbors of a node), yet more sophisticated operations are desirable for several Web analyses. We present a compact Web graph representation that, in addition, supports reverse navigation (to the nodes pointing to the given one). The standard approach to achieve this is to represent the graph and its transpose, which basically doubles the space requirement. Our structure, instead, represents the adjacency list using a compact sequence representation that allows finding the positions where a given node v is mentioned, and answers reverse navigation using that primitive. This is combined with a previous proposal based on grammar compression of the adjacency list. The combination yields interesting algorithmic problems. As a result, we achieve the smallest graph representation reported in the
Cell Probe Lower Bounds For Succinct Data Structures
"... In this paper, we consider several static data structure problems in the deterministic cell probe model. We develop a new technique for proving lower bounds for succinct data structures, where the redundancy in the storage can be small compared to the informationtheoretic minimum. In fact, we succee ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
In this paper, we consider several static data structure problems in the deterministic cell probe model. We develop a new technique for proving lower bounds for succinct data structures, where the redundancy in the storage can be small compared to the informationtheoretic minimum. In fact, we succeed in matching (up to constant factors) the lower order terms of the existing data structures with the lower order terms provided by our lower bound. Using this technique, we obtain (i) the first lower bound for the problem of searching and retrieval of a substring in text; (ii) a cell probe lower bound for the problem of representing permutation π with queries π(i) and π−1 (i) thatmatchesthelower order term of the existing data structures, and (iii) a lower bound for representing binary matrices that is also matches upper bounds for some set of parameters. The nature of all these problems is that we are to implement two operations that are in a reciprocal relation to each other (search and retrieval, computing forward and inverse element, operations on rows and columns of a matrix). As far as we know, this paper is the first to provide an insight into such problems. 1