Distributed algorithms for ultrasparse spanners and linear size skeletons

We present efficient algorithms for computing very sparse low distortion spanners in distributed networks and prove some non-trivial lower bounds on the tradeoff between time, sparseness, and distortion. All of our algorithms assume a synchronized distributed network, where relatively short messages may be communicated in each time step. Our first result is a fast distributed algorithm for finding an O(2log n log n)-spanner with size O(n). Besides being nearly optimal in time and distortion, this algorithm appears to be the first that constructs an O(n)-size skeleton without requiring unbounded length messages or time proportional to the diameter of the network. Our second result is a new class of efficiently constructible (, )-spanners called Fibonacci spanners whose distortion improves with the distance being approximated. At their sparsest Fibonacci spanners can have nearly linear size, namely O(n(log log n)), where = (1 + 5)/2 is the golden ratio. As the distance increases the mu...

• Type: Journal
• Year: 2010
• Where: DC
• Authors: Seth Pettie
• Keywords: Algorithm, DC 2001, DC 2010, Distortion, Distributed Network