Computing Diameter in the Streaming and Sliding-Window Models

We investigate the diameter problem in the streaming and slidingwindow models. We show that, for a stream of n points or a sliding window of size n, any exact algorithm for diameter requires (n) bits of space. We present a simple -approximation6 algorithm for computing the diameter in the streaming model. Our main result is an -approximation algorithm that maintains the diameter in two dimensions in the sliding-window model using O( 1 3/2 log3 n(log R+log log n+ log 1 )) bits of space, where R is the maximum, over all windows, of the ratio of the diameter to the minimum non-zero distance between any two points in the window.

• Type: Journal
• Year: 2004
• Where: ALGORITHMICA
• Authors: Joan Feigenbaum, Sampath Kannan, Jian Zhang 0004
• Keywords: ALGORITHMICA 2004, Diameter Problem, Simple -approximation6 Algorithm, Sliding Window