Succincter

Pătraşcu, Mihai

doi:10.1109/focs.2008.83

Cited by 111 publications

(76 citation statements)

References 18 publications

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“…Since the query algorithm accesses O(1) microtrees, the overall running time is O(k). Finally, the lower order terms that arise in various substructures above, such as FIDs and auxiliary structures for tree representations, which are independent of k, can be made O(n/(log n) O(1) ) using the ideas from [16]. Thus the overall space used is 5n + O(n log k/k) bits, for any parameter k = (log n) O(1) .…”

Section: Theorem 42mentioning

confidence: 99%

Encoding 2D Range Maximum Queries

Golin

Iacono

Kriz̧anc

et al. 2011

Algorithms and Computation

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We consider the two-dimensional range maximum query (2D-RMQ) problem: given an array containing elements from an ordered set, encode the array so that the position of the maximum element in any specified range of rows and range of columns can be found efficiently. We focus on determining the effective entropy of 2D-RMQ, i.e., how many bits are needed to encode an array so that 2D-RMQ queries can be answered without accessing the array. We give tight upper and lower bounds on the expected effective entropy for the case when A contains independent identically-distributed random values, and give new upper and lower bounds for the case when the array contains few rows. The latter results improve upon the upper and lower bounds by Brodal et al. [4]. We also give some efficient data structures for 2D-RMQ whose space usage is close to the effective entropy.

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Section: Theorem 42mentioning

confidence: 99%

Encoding 2D Range Maximum Queries

Golin

Iacono

Kriz̧anc

et al. 2011

Algorithms and Computation

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“…The following lemma presents a space/query time tradeoff bound for supporting rank and select on bit vectors that are weaker than that of Pǎtraşcu [18]. However, our data structure is much simpler, since we do not need it to be succinct.…”

Section: Decreasing the Spacementioning

confidence: 99%

Weighted Ancestors in Suffix Trees

Gawrychowski

Lewenstein

Nicholson

2014

Algorithms - ESA 2014

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Abstract. The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalization to weighted trees, a.k.a. the weighted ancestor problem, has been extensively explored and successfully reduced to the predecessor problem. It is known that any solution for both problems with an input set from a polynomially bounded universe that preprocesses a weighted tree in O(n polylog(n)) space requires Ω(log log n) query time. Perhaps the most important and frequent application of the weighted ancestors problem is for suffix trees. It has been a long-standing open question whether the weighted ancestors problem has better bounds for suffix trees. We answer this question positively: we show that a suffix tree built for a text w[1..n] can be preprocessed using O(n) extra space, so that queries can be answered in O(1) time. Thus we improve the running times of several applications. Our improvement is based on a number of data structure tools and a periodicity-based insight into the combinatorial structure of a suffix tree.

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“…Lemma 1 (Pǎtraşcu [15]). A bit string can be represented in n+O(n/(log n) 2 ) bits such that select 1 and rank 1 can be supported in O(1) time.…”

Section: Preliminariesmentioning

confidence: 99%

Improved Practical Compact Dynamic Tries

Poyias

Raman

2015

String Processing and Information Retrieval

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Abstract. We consider the problem of implementing a dynamic trie with an emphasis on good practical performance. For a trie with n nodes with an alphabet of size σ, the information-theoretic lower bound is n log σ + O(n) bits. The Bonsai data structure [1] supports trie operations in O(1) expected time (based on assumptions about the behaviour of hash functions). While its practical speed performance is excellent, its space usage of (1 + )n(log σ + O(log log n)) bits, where is any constant > 0, is not asymptotically optimal. We propose an alternative, m-Bonsai, that uses (1 + )n(log σ + O(1)) bits in expectation, and supports operations in O(1) expected time (again based on assumptions about the behaviour of hash functions). We give a heuristic implementation of mBonsai which uses considerably less memory and is slightly faster than the original Bonsai.

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Succincter

Cited by 111 publications

References 18 publications

Encoding 2D Range Maximum Queries

Encoding 2D Range Maximum Queries

Weighted Ancestors in Suffix Trees

Improved Practical Compact Dynamic Tries

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