# Lower Bounds for Sorted Geometric Queries in the I/O Model

@inproceedings{Afshani2012LowerBF, title={Lower Bounds for Sorted Geometric Queries in the I/O Model}, author={Peyman Afshani and Norbert Zeh}, booktitle={ESA}, year={2012} }

We study sorted geometric query problems, a class of problems that, to the best of our knowledge and despite their applications, have not received much attention so far. Two of the most prominent problems in this class are angular sorting queries and sorted K-nearest neighbour queries. The former asks us to preprocess an input point set S in the plane so that, given a query point q, the clockwise ordering of the points in S around q can be computed efficiently. In the latter problem, the output…

## One Citation

### Permuting and Batched Geometric Lower Bounds in the I/O Model

- Computer Science, MathematicsESA
- 2017

This work proves a general simulation result that essentially shows that any permutation algorithm that does alpha*N/B I/Os (resp. to remove a fraction of the existing duplicates) can be simulated with an algorithm thatdoes alpha phases where each phase reads and writes each element once, but using a factor alpha smaller block size.

## References

SHOWING 1-10 OF 15 REFERENCES

### Space-Query-Time Tradeoff for Computing the Visibility Polygon

- Computer ScienceFAW
- 2009

This paper considers the problem of computing VP for any query point efficiently, with some additional preprocessing phase, and shows for a query point q, VP (q) can be computed in logarithmic time using O (n 4) space and O ( n 4 logn ) preprocessing time.

### Optimal halfspace range reporting in three dimensions

- Computer ScienceSODA
- 2009

It is shown that n points in 3-d can be stored in a linear-space data structure so that all k points inside a query halfspace can be reported in O(log n + k) time.

### I/O-efficient point location using persistent B-trees

- Computer ScienceALENEX
- 2003

An extensive experimental evaluation shows that, on a range of real-world Geographic Information Systems (GIS) data, the developed structure uses a similar number of I/Os as the structure of Vahrenhold and Hinrichs to answer a query, and on a synthetically generated worst-case dataset the structure uses significantly fewer I/ Os.

### Filtering search: A new approach to query-answering

- Computer Science, Mathematics24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
- 1983

We introduce a new technique for solving problems of the following form: preprocess a set of objects so that those satisfying a given property with respect to a query object can be listed very…

### Worst-case optimal algorithms for constructing visibility polygons with holes

- Computer Science, MathematicsSCG '86
- 1986

A worst-ease lower bound of N(n 4) for explicitly computing the boundary of the visibility polygon from a line segment in the presence of other line segments is established, and an optimal algorithm to construct the boundary is designed.

### Lectures on discrete geometry

- MathematicsGraduate texts in mathematics
- 2002

This book is primarily a textbook introduction to various areas of discrete geometry, in which several key results and methods are explained, in an accessible and concrete manner, in each area.

### An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set

- MathematicsInf. Process. Lett.
- 1972

### Visibility of disjoint polygons

- Computer Science, MathematicsAlgorithmica
- 2005

This work shows how to build, in O(n2) time and space, a data structure from which inO(n) time the authors can compute the visibility polygon of a given point with respect to the polygon collection, implying that the shortest path that connects two points in the plane and avoids the polygons in their collection can be computed inO (n 2) time.

### Ordered and unordered top-K range reporting in large data sets

- Computer ScienceSODA '11
- 2011

A linear-size data structure is constructed that achieves a query bound of O(n + fK/B) I/Os and it is shown that it is the requirement that the <i>K</i> smallest elements be reported in sorted order which makes the problem hard.