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Optimal Dynamic Sequence Representations
"... We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string S[1, n] over alphabet [1..σ] in time O(lg n / lg lg n), which is optimal. The time is worstcase for the queries and amortized for the updates. This complexity is bette ..."
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We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string S[1, n] over alphabet [1..σ] in time O(lg n / lg lg n), which is optimal. The time is worstcase for the queries and amortized for the updates. This complexity is better than the best previous ones by a Θ(1 + lg σ / lg lg n) factor. Our structure uses nH0(S) + O(n + σ(lg σ + lg 1+ε n)) bits, where H0(S) is the zeroorder entropy of S and 0 < ε < 1 is any constant. This space redundancy over nH0(S) is also better, almost always, than that of the best previous dynamic structures, o(n lg σ)+O(σ(lg σ+lg n)). We can also handle general alphabets in optimal time, which has been an open problem in dynamic sequence representations.
Suffix trays and suffix trists: structures for faster text indexing
 In Proc. 33rd ICALP, LNCS 4051
, 2006
"... Abstract. Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time [3, 5–7]. However, when it comes to answering queries, the prior does so in O(m log Σ) time, where m is the query size, Σ  is t ..."
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Abstract. Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time [3, 5–7]. However, when it comes to answering queries, the prior does so in O(m log Σ) time, where m is the query size, Σ  is the alphabet size, and the latter does so in O(m + log n), where n is the text size. We propose a novel way of combining the two into, what we call, a suffix tray. The space and construction time remain linear and the query time improves to O(m + log Σ). We also consider the online version of indexing, where the indexing structure continues to update the text online and queries are answered in tandem. Here we suggest a suffix trist, a cross between a suffix tree and a suffix list. It supports queries in O(m + log Σ). The space and text update time of a suffix trist are the same as for the suffix tree or the suffix list. 1
Online indexing for general alphabets via predecessor queries on subsets of an ordered list
 In Proc. FOCS
, 2012
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On (Dynamic) Range Minimum Queries in External Memory
"... Abstract. We study the onedimensional range minimum query (RMQ) problem in the external memory model. We provide the first spaceoptimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + N+Q ..."
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Abstract. We study the onedimensional range minimum query (RMQ) problem in the external memory model. We provide the first spaceoptimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + N+Q
CrossDocument Pattern Matching
, 2013
"... We study a new variant of the pattern matching problem called crossdocument pattern matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants ..."
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We study a new variant of the pattern matching problem called crossdocument pattern matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted ancestor problem.
Fullfledged RealTime Indexing for Constant Size Alphabets
"... Abstract. In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet of constant size. Each new symbol can be prepended to T in O(1) expected worstcase time. At any moment, we can report all occurrences of a pattern P in the c ..."
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Abstract. In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet of constant size. Each new symbol can be prepended to T in O(1) expected worstcase time. At any moment, we can report all occurrences of a pattern P in the current text in O(P + k) time, where P  is the length of P and k is the number of occurrences. This resolves, under assumption of constant size alphabet, a longstanding open problem of existence of a realtime indexing method for string matching (see [2]). 1
3 Managing UnboundedLength Keys in ComparisonDriven Data Structures with Applications to OnLine Indexing∗
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CrossDocument Pattern MatchingI
"... We study a new variant of the pattern matching problem called crossdocument pattern matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variant ..."
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We study a new variant of the pattern matching problem called crossdocument pattern matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted ancestor problem.
Combining Digital Access and Parallel Partition for Quicksort and Quickselect
"... In this paper, we combine digital access to strings with parallel partition to enhance parallel quicksort and quickselect implementations. Previously, digital access had only been combined with sequential comparisonbased algorithms and data structures. We present broadly our approach, not only a ..."
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In this paper, we combine digital access to strings with parallel partition to enhance parallel quicksort and quickselect implementations. Previously, digital access had only been combined with sequential comparisonbased algorithms and data structures. We present broadly our approach, not only algorithmically but from the design and implementation point of view. Finally, we give some experimental results that indicate its effectiveness in practice. 1.