Range Selection and Median: Tight Cell Probe Lower Bounds and Adaptive Data Structures

Jørgensen, Allan Grønlund; Larsen, Kasper Green

doi:10.1137/1.9781611973082.63

Cited by 29 publications

(43 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that Lemma 6 essentially is a generalization of the results proved in the static range counting papers [6,3], simply phrased in terms of cell subsets answering many queries instead of communication complexity. Since the proof contains only few new ideas, we have deferred it to Section 5 and instead move on to the encoding and decoding procedures.…”

Section: The Set Of Incidence Vectorsmentioning

confidence: 95%

“…In [7] he reproved this bound using an elegant reduction from the communication game known as lop-sided set disjointness. Subsequently Jørgensen and Larsen [3] proved a matching bound for the strongly related problems of range selection and range median. Finally, as mentioned earlier, Pǎtraşcu [6] proved a max{t q , t u } = Ω((lg n/ lg lg n)…”

Section: The Cell Probe Modelmentioning

confidence: 99%

See 1 more Smart Citation

The cell probe complexity of dynamic range counting

Larsen

2012

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: The Set Of Incidence Vectorsmentioning

confidence: 95%

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…This problem has recently been studied intensively in its non-encoding version [5,6,9,10,14]. Jørgensen and Larsen [14] obtained a query time of O(lg k/ lg lg n+ lg lg n), very recently improved to O(lg k/ lg lg n) by Chan and Wilkinson [6], both using Θ(n) words, i.e., Ω(n lg n) bits. Jørgensen and Larsen [14] introduced the κ-capped range selection problem, where a parameter κ is given at preprocessing time, and the data structure only supports selection for ranks k ≤ κ.…”

Section: Introductionmentioning

confidence: 99%

“…Jørgensen and Larsen [14] obtained a query time of O(lg k/ lg lg n+ lg lg n), very recently improved to O(lg k/ lg lg n) by Chan and Wilkinson [6], both using Θ(n) words, i.e., Ω(n lg n) bits. Jørgensen and Larsen [14] introduced the κ-capped range selection problem, where a parameter κ is given at preprocessing time, and the data structure only supports selection for ranks k ≤ κ. They showed that even the one-sided κ-capped range selection problem requires query time Ω(lg k/ lg lg n) for structures using O(n polylog n) words, and the result of Chan and Wilkinson is therefore the best possible.…”

Section: Introductionmentioning

confidence: 99%

“…They showed that even the one-sided κ-capped range selection problem requires query time Ω(lg k/ lg lg n) for structures using O(n polylog n) words, and the result of Chan and Wilkinson is therefore the best possible. Although the problems we consider are different in essential ways, we borrow some techniques, most notably that of shallow cuttings [6,14], in some of our results.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Encodings for Range Selection and Top-k Queries

Grossi

Iacono

Navarro

et al. 2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We study the problem of encoding the positions the top-k elements of an array A[1..n] for a given parameter 1 ≤ k ≤ n. Specifically, for any i and j, we wish create a data structure that reports the positions of the largest k elements in A[i..j] in decreasing order, without accessing A at query time. This is a natural extension of the well-known encoding range-maxima query problem, where only the position of the maximum in A[i..j] is sought, and finds applications in document retrieval and ranking. We give (sometimes tight) upper and lower bounds for this problem and some variants thereof.

show abstract

Adaptive Data Structures for 2D Dominance Colored Range Counting

Gao¹

2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Range Selection and Median: Tight Cell Probe Lower Bounds and Adaptive Data Structures

Cited by 29 publications

References 0 publications

The cell probe complexity of dynamic range counting

The cell probe complexity of dynamic range counting

Encodings for Range Selection and Top-k Queries

Adaptive Data Structures for 2D Dominance Colored Range Counting

Contact Info

Product

Resources

About