Publisher's Synopsis
Excerpt from Very Fast Algorithms for the Area of the Union of Many Circles
The problem of estimating the area of the union of many circles in the plane was first posed by [shamos, We present here an 0(n2) deterministic and an o(u) probabilistic algorithm for solving the problem. The recent work of [karp, Luby, 83] on estimating the failure probability of an n-component system helped us a lot in stating the algorithm and formulating the proof of fast convergence. The probabilistic algorithm can be modified to compute the area of the union of other planar objects (of fixed description) e.g. Triangles or boxes. The time is again o(u). The algorithm can also be extended to compute the volume of the union of n spheres in k dimensions, in time 0(nk). The algorithm has similar time complexity for k-dimensional objects other than spheres, provided that each object has a fixed description (not dependent on n).
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