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ISTC-CC Abstract
Parallel Probabilistic Tree Embeddings, k-Median, and
Buy-at-Bulk Network Design
Proceedings of the 24th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'12), June 2012.
Guy Blelloch, Anupam Gupta, and Kanat Tangwongsan
Carnegie Mellon University
This paper presents parallel algorithms for embedding an arbitrary n-point metric space into a distribution of dominating trees with O(log n) expected stretch. Such embedding has proved useful in the design of many approximation algorithms in the sequential setting. We give a parallel algorithm that runs in O(n2 log n) work and O(log2 n) depth—these bounds are independent of Δ = maxx,y d(x,y) / minx≠y d(x,y), the ratio of the largest to smallest distance. Moreover, when Δ is exponentially bounded (Δ ≤ 2O(n)), our algorithm can be improved to O(n2) work and O(log2 n) depth. Using these results, we give an RNC O(log k)-approximation algorithm for k-median and an RNC O(log n)-approximation for buy-at-bulk network design. The k-median algorithm is the first RNC algorithm with non-trivial guarantees for arbitrary values of k, and the buy-at-bulk result is the first parallel algorithm for the problem.
KEYWORDS: Parallel algorithms, probabilistic tree embedding, kmedian, buy-at-bulk network design
FULL PAPER: pdf