# Efficient algorithms for Identifying All Maximal Isothetic Empty Rectangles in VLSI Layout Design

@inproceedings{Nandy1990EfficientAF, title={Efficient algorithms for Identifying All Maximal Isothetic Empty Rectangles in VLSI Layout Design}, author={Subhas C. Nandy and Bhargab B. Bhattacharya and S. Ray}, booktitle={FSTTCS}, year={1990} }

In this paper, we consider the following problem of computational geometry which has direct applications to VLSI layout design : given a set of n isothetic solid rectangles on a rectangular floor, identify all maximal-empty-rectangles (MER's). A tighter upper bound on the number of MER's is derived. A new algorithm based on interval trees for identifying all MER's is then presented which runs in O(nlogn+R) time in the worst case and in O(nlogn) time in the average case, where R denotes the…

## 19 Citations

### Efficient algorithm for identifying a pair of maximal empty rectangles of maximum total area amidst a point set

- Mathematics, Computer Science
- 2016

If the authors try to find two disjoint MER whose union is maximum, the by line sweep technique it can be solved in O(R + n log n) time, where R is the maximum number of MER’s.

### A unified algorithm for finding maximum and minimum object enclosing rectangles and cuboids

- Mathematics
- 1995

### Location of the Largest Empty Rectangle among Arbitrary Obstacles

- MathematicsFSTTCS
- 1994

This paper outlines the following generalization of the classical maximal-empty-rectangle (MER) problem: given n arbitrarily-oriented non-intersecting line segments of finite length on a rectangular…

### Recognizing the Largest Empty Circle and Axis-Parallel Rectangle in a Desired Location

- Computer ScienceArXiv
- 2010

In this paper, we study the query version of the largest empty space recognition problem. Here, a set of n points P is given in a bounded 2D region. The objective is to preprocess P such that given…

### Extensions of the Maximum Bichromatic Separating Rectangle Problem

- Computer Science, MathematicsCCCG
- 2021

The solution to MBSR-C is an O(m2+n)-time algorithm that involves an optimized scanning of all candidate circle arcs for locations of potential optimal solutions and a clever staircase sweep approach to improve the current known time bounds.

### Finding a largest rectangle inside a digital object and rectangularization

- MathematicsJ. Comput. Syst. Sci.
- 2018

### Finding Largest Rectangle Inside a Digital Object

- Computer ScienceCTIC
- 2016

We present a combinatorial algorithm which runs in $$On \log n$$Onlogn time to find largest rectangle LR inside a given digital object without holes, n being the number of pixels on the contour of…

### On Packing Almost Half of a Square with Anchored Rectangles: A Constructive Approach

- MathematicsArXiv
- 2014

The longstanding conjecture has been that at least half of $U$ can be covered when anchored rectangles are properly placed, and Dumitrescu and T{\'o}th \cite{Dumit Rescu2012} have shown a construction method that can cover at least $0.09121$ of the area.

## References

SHOWING 1-10 OF 18 REFERENCES

### Computing the Largest Empty Rectangle

- Computer ScienceSIAM J. Comput.
- 1984

A divide-and-conquer approach similar to the ones used by Strong and Bentley is used and a new notion of Voronoi diagram is introduced along with a method for efficient computation of certain functions over paths of a tree.

### An Optimal Worst Case Algorithm for Reporting Intersections of Rectangles

- Computer ScienceIEEE Transactions on Computers
- 1980

This paper investigates the problem of reporting all intersecting pairs in a set of n rectilinearly oriented rectangles in the plane and describes an algorithm that solves this problem in worst case time proportional to n lg n + k, where k is the number of interesecting pairs found.

### Geometric intersection problems

- Computer Science, Mathematics17th Annual Symposium on Foundations of Computer Science (sfcs 1976)
- 1976

An O(N log N) algorithm is given to determine whether any two intersect and use it to detect whether two simple plane polygons intersect and to show that the Simplex method is not optimal.

### Algorithms for Reporting and Counting Geometric Intersections

- Computer Science, MathematicsIEEE Transactions on Computers
- 1979

Algorithms that count the number of pairwise intersections among a set of N objects in the plane and algorithms that report all such intersections are given.

### Fast algorithms for computing the largest empty rectangle

- PhysicsSCG '87
- 1987

The first algorithm for computing the largest-area empty rectangle is optimal within a multiplicative constant and the two algorithms for computing such a rectangle can be modified to compute thelargest-perimeter rectangle in memory space.

### Computational Geometry—A Survey

- Computer Science, MathematicsIEEE Transactions on Computers
- 1984

We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis of algorithms. This newly emerged area…

### Corner Stitching: A Data-Structuring Technique for VLSI Layout Tools

- Computer ScienceIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
- 1984

The algorithms are presented under a simplified model of VLSI circuits, and the storage requirements of the structure are discussed.

### Analysis of strategies for constructive general block placement

- Computer ScienceIEEE Trans. Comput. Aided Des. Integr. Circuits Syst.
- 1988

The problem of general block placement in VLSI is considered, using the constructive approach in which blocks are selected and located one at a time, and it is shown that the squared Euclidean and the rectilinear metrics are preferable to the Euclidesan one.