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337
Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence
 In Proc. FOCS’07
, 2007
"... We show that any deterministic datastream algorithm that makes a constant number of passes over the input and gives a constant factor approximation of the length of the longest increasing subsequence in a sequence of length n must use space Ω ( √ n). This proves a conjecture made by Gopalan, Jayra ..."
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We show that any deterministic datastream algorithm that makes a constant number of passes over the input and gives a constant factor approximation of the length of the longest increasing subsequence in a sequence of length n must use space Ω ( √ n). This proves a conjecture made by Gopalan
The Communication and Streaming Complexity of Computing the Longest Common and Increasing Subsequences
, 2007
"... We consider the communication complexity of finding the longest increasing subsequence (LIS) of a string shared between two parties. We prove tight bounds forthe space complexity of randomized onepass streaming algorithms for this problem. Our bounds are parameterized in terms of the LIS of the i ..."
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Cited by 10 (0 self)
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We consider the communication complexity of finding the longest increasing subsequence (LIS) of a string shared between two parties. We prove tight bounds forthe space complexity of randomized onepass streaming algorithms for this problem. Our bounds are parameterized in terms of the LIS
Private Computation of the Longest Increasing Subsequence in Data Streams
"... In this paper, we study the problem of privately computing ordered statistics with the goal of monitoring sequential data streams. Despite the broad series of techniques for timeseries monitoring, only few works provide provable privacy guarantees employing the formal notion of differential priva ..."
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solutions estimate the length of the LIS using block decomposition and local approximation techniques. We provide a rigorous analysis to bound the approximation error of our algorithms in terms of privacy level and length of the stream. 1.
Finding Longest Increasing and Common Subsequences in Streaming Data
, 2003
"... In this paper, we present algorithms and lower bounds for the Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS) problems in the data streaming model. ..."
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Cited by 16 (0 self)
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In this paper, we present algorithms and lower bounds for the Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS) problems in the data streaming model.
On Distance to Monotonicity and Longest Increasing Subsequence of a Data Stream
"... In this paper we consider problems related to the sortedness of a data stream. First we investigate the problem of estimating the distance to monotonicity; given a sequence of length n, we give a deterministic (2 + ɛ)approximation algorithm for estimating its distance to monotonicity in space O ( 1 ..."
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fooling set approach to prove that any O(1)pass deterministic streaming algorithm that approximates the length of the longest increasing subsequence within 1 + ɛ requires Ω ( √ n) space. This proves the conjecture in [3] and matches the current upper bound. 1
Approximating the Longest Increasing Sequence and Distance from . . .
, 2006
"... We revisit the wellstudied problem of estimating the sortedness of a data stream. We study the complementary problems of estimating the edit distance from sortedness (Ulam distance) and estimating the length of the longest increasing sequence (LIS). We present the first sublinear space algorithms ..."
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We revisit the wellstudied problem of estimating the sortedness of a data stream. We study the complementary problems of estimating the edit distance from sortedness (Ulam distance) and estimating the length of the longest increasing sequence (LIS). We present the first sublinear space algorithms
Bounds on the complexity of the longest common subsequence problem
 Journal of the ACM
, 1976
"... ABSTRACT The problem of finding a longest common subsequence of two strings is discussed This problem arises in data processing applications such as comparing two files and in genetic applications such as studying molecular evolution The ddlqculty of computing a longest common subsequence of two str ..."
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Cited by 77 (1 self)
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to the product of the lengths of the two strings A general lower bound as a function of the ratio of alphabet size to string length is derived The case where comparisons between symbols of the same string are forbidden is also considered and it is shown that this problem is of linear complexity for a two
On the Longest Common Parameterized Subsequence
"... The wellknown problem of the longest common subsequence (LCS), of two strings of lengths n and m respectively, is O(nm)time solvable and is a classical distance measure for strings. Another wellstudied string comparison measure is that of parameterized matching, where two equallength strings are ..."
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with other distance measures, as these turn out to be natural problems, e.g., Hamming distance, and a bounded version of editdistance. Several algorithms have been proposed for these problems. In this paper we consider the longest common parameterized subsequence problem which combines the LCS measure
A faster algorithm for computing a longest common increasing subsequence
 Research Report MPII20051007, MaxPlanckInstitut für Informatik, Stuhlsatzenhausweg 85, 66123
, 2005
"... Abstract. We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where m ≥ n, we present an algorithm with an outputdependent expected running time of O((m + nℓ)loglogσ + Sort) and O(m) space, where ℓ is the le ..."
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Abstract. We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where m ≥ n, we present an algorithm with an outputdependent expected running time of O((m + nℓ)loglogσ + Sort) and O(m) space, where ℓ
Results 1  10
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337