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Results 1 - 10
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351
Time-Space Trade-Offs for Longest Common Extensions
- In Proc. 23rd CPM, LNCS
, 2012
"... We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. An LCE query takes a pair (i, j) of indices in T and returns the length of the longest common prefix of the suffixes of T starting at positions i and j. ..."
Abstract
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Cited by 4 (3 self)
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. We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T. Given a parameter τ, 1 ≤ τ ≤ n, we show how to achieve either O(n/ τ) space and O(τ) query time, or O(n/τ) space and O(τ log
Locality-sensitive hashing scheme based on p-stable distributions
- In SCG ’04: Proceedings of the twentieth annual symposium on Computational geometry
, 2004
"... inÇÐÓ�Ò We present a novel Locality-Sensitive Hashing scheme for the Approximate Nearest Neighbor Problem underÐÔnorm, based onÔstable distributions. Our scheme improves the running time of the earlier algorithm for the case of theÐnorm. It also yields the first known provably efficient approximate ..."
Abstract
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Cited by 521 (8 self)
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NN algorithm for the caseÔ�. We also show that the algorithm finds the exact near neigbhor time for data satisfying certain “bounded growth ” condition. Unlike earlier schemes, our LSH scheme works directly on points in the Euclidean space without embeddings. Consequently, the resulting query time
Time-Space Trade-Offs for Predecessor Search (Extended Abstract)
, 2006
"... We develop a new technique for proving cell-probe lower bounds for static data structures. Previous lower bounds used a reduction to communication games, which was known not to be tight by counting arguments. We give the first lower bound for an explicit problem which breaks this communication compl ..."
Abstract
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Cited by 3 (1 self)
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complexity barrier. In addition, our bounds give the first separation between polynomial and near linear space. Such a separation is inherently impossible by communication complexity. Using our lower bound technique and new upper bound constructions, we obtain tight bounds for searching predecessors among a
Optimal Time-Space Trade-Offs for Non-Comparison-Based Sorting ∗
"... We study the problem of sorting n integers of w bits on a unit-cost RAM with word size w, and in particular consider the time-space trade-off (product of time and space in bits) for this problem. For comparison-based algorithms, the time-space complexity is known to be Θ(n 2). A result of Beame show ..."
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We study the problem of sorting n integers of w bits on a unit-cost RAM with word size w, and in particular consider the time-space trade-off (product of time and space in bits) for this problem. For comparison-based algorithms, the time-space complexity is known to be Θ(n 2). A result of Beame
Lower bounds on near neighbor search via metric expansion
- CoRR
"... In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points within a certain distance r. We then look at various notions o ..."
Abstract
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Cited by 14 (1 self)
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, the bound drops exponentially in t. We show a much stronger (tight) time-space tradeoff for the class of dynamic low contention data structures. These are data structures that supports updates in the data set and that do not look up any single cell too often. 1 1
A geometric approach to lower bounds for approximate near-neighbor search and partial match
- In Proc. 49th IEEE Symposium on Foundations of Computer Science (FOCS
, 2008
"... This work investigates a geometric approach to proving cell probe lower bounds for data structure problems. We consider the approximate nearest neighbor search problem on the Boolean hypercube ({0, 1} d, ‖ · ‖1) with d = Θ(log n). We show that any (randomized) data structure for the problem that a ..."
Abstract
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Cited by 16 (2 self)
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bound holds for the near neighbor problem, where the algorithm knows in advance a good approximation to the distance to the nearest neighbor. Additionally, it is an average case lower bound for the natural distribution for the problem. Our approach also gives the same bound for (2 − 1)-approximation
Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in HighDimensions*
"... Abstract We present an algorithm for the c-approximate near-est neighbor problem in a d-dimensional Euclidean space,achieving query time of O(dn1/c 2+o(1)) and space O(dn + n1+1/c 2+o(1)). This almost matches the lower bound for hashing-based algorithm recently obtained in [27]. We alsoobtain a spac ..."
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Abstract We present an algorithm for the c-approximate near-est neighbor problem in a d-dimensional Euclidean space,achieving query time of O(dn1/c 2+o(1)) and space O(dn + n1+1/c 2+o(1)). This almost matches the lower bound for hashing-based algorithm recently obtained in [27]. We alsoobtain a
Higher lower bounds for near-neighbor and further rich problems
- in Proc. 47th IEEE Symposium on Foundations of Computer Science (FOCS
"... We convert cell-probe lower bounds for polynomial space into stronger lower bounds for near-linear space. Our technique applies to any lower bound proved through the richness method. For example, it applies to partial match, and to near-neighbor problems, either for randomized exact search, or for d ..."
Abstract
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Cited by 23 (2 self)
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We convert cell-probe lower bounds for polynomial space into stronger lower bounds for near-linear space. Our technique applies to any lower bound proved through the richness method. For example, it applies to partial match, and to near-neighbor problems, either for randomized exact search
A Lower Bound on the Complexity of Approximate Nearest-Neighbor Searching on the Hamming Cube
- In Proc. 31th Annual ACM Symposium on Theory of Computing (STOC’99
, 1999
"... We consider the nearest-neighbor problem over the d-cube: given a collection of points in {0, 1} d , find the one nearest to a query point (in the L 1 sense). We establish a lower bound of###90 log d/ log log log d) on the worst-case query time. This result holds in the cell probe model with ( ..."
Abstract
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Cited by 19 (3 self)
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We consider the nearest-neighbor problem over the d-cube: given a collection of points in {0, 1} d , find the one nearest to a query point (in the L 1 sense). We establish a lower bound of###90 log d/ log log log d) on the worst-case query time. This result holds in the cell probe model
Nearest Neighbor Search in Lower Dimensional Flats
"... In order to improve efficiency in Approximate Near-est Neighbor (ANN) search, we exploit the structure of the input data by considering points that are dis-tributed almost uniformly on flats of varying, fixed di-mension. These flats are distributed uniformly within a bounding sphere of radius 1. We ..."
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employ an existing mapping that transforms Nearest Flat search to Near-est point search. Our algorithm, using linear space in the number of points, returns an (1 + )-approximate neighbor in expected time O(c logm), where m is the number of flats, c = O∗((λ2)−d 2), d is the ambient space dimension, λ
Results 1 - 10
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351
