Succinct Representation of Balanced Parentheses and Static Trees

Munro, J. Ian; Raman, Venkatesh

doi:10.1137/s0097539799364092

Cited by 269 publications

(268 citation statements)

References 10 publications

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“…For each such point, the corresponding k value is stored. Each of these four structures requires n log n(1 + o(1)) bits of space if they are represented succinctly, for example, using the balanced parenthesis representation [14] for the tries. For Range, the data structure of Chazelle [2] permits two-dimensional range searching in a grid of n pairs of integers in the range…”

Section: The Lz-index Data Structurementioning

confidence: 99%

“…Both LZTrie and RevTrie use originally the balanced parenthesis representation [14], in which every node, represented by a pair of opening and closing parentheses, encloses its subtree. When we replace Range by RNode structure, the result is actually a "navigation" scheme that permits us moving back and forth from trie nodes to the corresponding preorder positions 4 , both in LZTrie and RevTrie.…”

Section: Lz-index As a Navigation Schemementioning

confidence: 99%

“…• par: the balanced parentheses representation [14] of LZTrie. In order to index the LZTrie leaves with xbw, we have to add a dummy child to each.…”

Section: Using the Xbw Transform To Represent Lztriementioning

confidence: 99%

“…In this way, the trie has n ′ 2n nodes. The space requirement is 4n + o(n) bits in the worst case if we use the Munro and Raman representation [14]. We use the bit 0 to represent '(' and 1 to represent ')'.…”

Section: Using the Xbw Transform To Represent Lztriementioning

confidence: 99%

“…In this part we define new data structures allowing the same navigation, yet reducing the original redundancy. In the second approach we combine the balanced parentheses representation of Munro and Raman [14] of the LZ78 trie with the xbw transform of Ferragina et al [3], whose powerful operations are useful for the LZ-index search algorithm.…”

Section: Introduction and Previous Workmentioning

confidence: 99%

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Reducing the Space Requirement of LZ-Index

Arroyuelo

Navarro

Sadakane

2006

Combinatorial Pattern Matching

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Abstract. The LZ-index is a compressed full-text self-index able to represent a text T 1...u , over an alphabet of size σ and with k-th order empirical entropy H k (T ), using 4uH k (T ) + o(u log σ ) bits for any k = o(log σ u). It can report all the occ occurrences of a pattern P 1...m in T in O(m 3 log σ + (m + occ) log u) worst case time. This is the only existing data structure of size O(uH k (T )) able of spending O(log u) time per occurrence reported. Its main drawback is the factor 4 in its space complexity, which makes it larger than other stateof-the-art alternatives. In this paper we present two different approaches to reduce the space requirement of LZ-index. In both cases we achieve (2 + ε)uH k (T ) + o(u log σ ) bits of space, for any constant ε > 0, and we simultaneously improve the search time to O(m 2 log m + (m + occ) log u). Both indexes support displaying any subtext of length ℓ in optimal O(ℓ/ log σ u) time. In addition, we show how the space can be squeezed to (1 + ε)uH k (T ) + o(u log σ ) to obtain a structure with O(m 2 ) average search time for m 2 log σ u.

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Section: The Lz-index Data Structurementioning

confidence: 99%

Section: Lz-index As a Navigation Schemementioning

confidence: 99%

“…• par: the balanced parentheses representation [14] of LZTrie. In order to index the LZTrie leaves with xbw, we have to add a dummy child to each.…”

Section: Using the Xbw Transform To Represent Lztriementioning

confidence: 99%

Section: Using the Xbw Transform To Represent Lztriementioning

confidence: 99%

Section: Introduction and Previous Workmentioning

confidence: 99%

See 3 more Smart Citations

Reducing the Space Requirement of LZ-Index

Arroyuelo

Navarro

Sadakane

2006

Combinatorial Pattern Matching

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Fast in‐memory XPath search using compressed indexes

et al. 2013

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Artículo de publicación ISIExtensible Markup Language (XML) documents consist of text data plus structured data (markup). XPath allows to query both text and structure. Evaluating such hybrid queries is challenging. We present a system for in-memory evaluation of XPath search queries, that is, queries with text and structure predicates, yet without advanced features such as backward axes, arithmetics, and joins. We show that for this query fragment, which contains Forward Core XPath, our system, dubbed Succinct XML Self-Index (‘SXSI’), outperforms existing systems by 1–3 orders of magnitude. SXSI is based on state-of-the-art indexes for text and structure data. It combines two novelties. On one hand, it represents the XML data in a compact indexed form, which allows it to handle larger collections in main memory while supporting powerful search and navigation operations over the text and the structure. On the other hand, it features an execution engine that uses tree automata and cleverly chooses evaluation orders that leverage the speeds of the respective indexes. SXSI is modular and allows seamless replacement of its indexes. This is demonstrated through experiments with (1) a text index specialized for search of bio sequences, and (2) a word-based text index specialized for natural language search.Fondecyt, Chile 1-11006

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Efficient Implementation of Rank and Select Functions for Succinct Representation

Kim

et al. 2005

Experimental and Efficient Algorithms

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Abstract. Succinct representation is a space-efficient method to represent n discrete objects by O(n) bits. In order to access directly the ith object of succinctly represented data structures in constant time, two fundamental functions, rank and select, are commonly used. However, little efforts were made on analyzing practical behaviors of these functions despite their importance for succinct representations.In this paper we analyze the behavior of Clark's algorithm which is the only one to support select in constant time using o(n)-bit space of extra space, and show that the performance of Clark's algorithm gets worse as the number of 1's in a bit-string becomes fewer and there exists a worst case in which a large amount of operations are needed. Then, we propose two algorithms that overcome the drawbacks of Clark's. These algorithms take constant time for select, and one uses o(n) bits for extra space and the other uses n + o(n) bits in the worst case. Experimental results show that our algorithms compute select faster than Clark's.

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Succinct Representation of Balanced Parentheses and Static Trees

Cited by 269 publications

References 10 publications

Reducing the Space Requirement of LZ-Index

Reducing the Space Requirement of LZ-Index

Fast in‐memory XPath search using compressed indexes

Efficient Implementation of Rank and Select Functions for Succinct Representation

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