The cell probe complexity of dynamic data structures

Fredman, Michael L.; Saks, Michael

doi:10.1145/73007.73040

Cited by 257 publications

(188 citation statements)

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“…In particular, we analyze a limited class of single-round Monte Carlo algorithms for the top-k problem, and prove a lower bound on the cell-probe complexity [23,14] of algorithms in this model, which is very close to our upper bound in this class.…”

Section: Our Resultsmentioning

confidence: 59%

“…In some cases, it is more convenient to analyze the cell probe complexity of algorithms [23,14] rather than directly analyze their communication complexity. We define the cell probe complexity of an algorithm as the maximum number of input cells accessed by a single node.…”

Section: Complexity Measuresmentioning

confidence: 99%

“…In this section we give a lower bound on the total cell probe complexity [23,14] of randomized algorithms for the top-k problem. For a restricted settings, we can deduce a lower bound on the individual communication complexity of such randomized algorithms.…”

Section: A Lower Bound On the Total Cell-probe Complexitymentioning

confidence: 99%

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Approximate distributed top-k queries

Patt-Shamir

Shafrir

2008

Distrib. Comput.

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We consider a distributed system where each node keeps a local count for items (similar to elections where nodes are ballot boxes and items are candidates). A top-k query in such a system asks which are the k items whose global count, across all nodes in the system, is the largest. In this paper we present a MonteCarlo algorithm that outputs, with high probability, a set of k candidates which approximates the top-k items. The algorithm is motivated by sensor networks in that it focuses on reducing the individual communication complexity. In contrast to previous algorithms, the communication complexity depends only on the global scores and not on the partition of scores among nodes. If the number of nodes is large, our algorithm dramatically reduces the communication complexity when compared with deterministic algorithms. We show that the complexity of our algorithm is close to a lower bound on the cell-probe complexity of any non-interactive top-k approximation algorithm. We show that for some natural global distributions (such as the Geometric or Zipf distributions), our algorithm needs only polylogarithmic number of communication bits per node.

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Section: Our Resultsmentioning

confidence: 59%

Section: Complexity Measuresmentioning

confidence: 99%

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Approximate distributed top-k queries

Patt-Shamir

Shafrir

2008

Distrib. Comput.

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“…Each cell of the data structure is identified by an integer address, which is assumed to fit in w bits, i.e. each address is amongst [2 w ] = {0, . .…”

Section: The Cell Probe Modelmentioning

confidence: 99%

“…In their seminal paper [2], Fredman and Saks introduced the celebrated chronogram technique. They applied their technique to the partial sums problem and obtained a lower bound stating that t q = Ω(lg n/ lg(wt u )), where t q is the query time and t u the update time.…”

Section: The Cell Probe Modelmentioning

confidence: 99%

The cell probe complexity of dynamic range counting

Larsen

2012

Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing

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In this paper we develop a new technique for proving lower bounds on the update time and query time of dynamic data structures in the cell probe model. With this technique, we prove the highest lower bound to date for any explicit problem, namely a lower bound of tq = Ω((lg n/ lg(wtu))2 ). Here n is the number of update operations, w the cell size, tq the query time and tu the update time. In the most natural setting of cell size w = Θ(lg n), this gives a lower bound of tq = Ω((lg n/ lg lg n)2 ) for any polylogarithmic update time. This bound is almost a quadratic improvement over the highest previous lower bound of Ω(lg n), due to Pǎtraşcu and Demaine [SICOMP'06].We prove the lower bound for the fundamental problem of weighted orthogonal range counting. In this problem, we are to support insertions of two-dimensional points, each assigned a Θ(lg n)-bit integer weight. A query to this problem is specified by a point q = (x, y), and the goal is to report the sum of the weights assigned to the points dominated by q, where a point (x , y ) is dominated by q if x ≤ x and y ≤ y. In addition to being the highest cell probe lower bound to date, the lower bound is also tight for data structures with update time tu = Ω(lg 2+ε n), where ε > 0 is an arbitrarily small constant.

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Backtracking

Apostolico

Italiano

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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The sections in this article are Models of Computation The Set Union Problem The Worst‐Case Time Complexity of a Single Operation The Set Union Problem With Deunions Split and The Set Union Problem on Intervals The Set Union Problem With Unlimited Backtracking

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The cell probe complexity of dynamic data structures

Abstract: Dynamic data stNcture problems involve the representation of data in memory in such a way as to permit certain types of modifications of the data (updates) and certain types of questions about the data (queries).This paradigm encompasses many fimdamental problems in computer science.

Cited by 257 publications

References 17 publications

Approximate distributed top-k queries

Approximate distributed top-k queries

The cell probe complexity of dynamic range counting

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