# Computing the volume of the union of cubes

Published

Journal Article

Let C be a set of n axis-aligned cubes in R 3 , and let U(C) denote the union of C. We present an algorithmthat can compute the volume of U(C) in time O(n 4/3 log n). The previously best known algorithm, by Overmars and Yap, computes the volume of the union ofany n axis-aligned boxes in R 3 in O(n 3/2 log n) time. Copyright 2007 ACM.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Kaplan, H; Sharir, M

### Published Date

- October 22, 2007

### Published In

- Proceedings of the Annual Symposium on Computational Geometry

### Start / End Page

- 294 - 301

### Digital Object Identifier (DOI)

- 10.1145/1247069.1247121

### Citation Source

- Scopus