# SEARCH

# ISTC-CC NEWSLETTER

# RESEARCH HIGHLIGHTS

Ling Liu's SC13 paper "Large Graph Processing Without the Overhead" featured by HPCwire.

ISTC-CC provides a listing of useful benchmarks for cloud computing.

Another list highlighting Open Source Software Releases.

Second GraphLab workshop should be even bigger than the first! GraphLab is a new programming framework for graph-style data analytics.

# ISTC-CC Abstract

**Parallel Probabilistic Tree Embeddings, k-Median, and **

Buy-at-Bulk Network Design

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*(*n*^{2} log *n*) work and *O*(log^{2} *n*) depthâ€”these bounds are independent of Δ = max_{x,y} d(x,y) / min_{x≠y} d(x,y), the ratio of the largest to smallest distance. Moreover, when Δ is exponentially bounded (Δ ≤ 2^{O(n)}), our algorithm can be improved to *O*(*n*^{2}) work and *O*(log^{2} *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**