# 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

**Iterative Row Sampling**

*54th Annual IEEE Symposium on Foundations of Computer Science (FOCS’13), October 2013.*

**Mu Li, Gary L. Miller, Richard Peng**

Carnegie Mellon University

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n X d matrix where n >> d, which allows one to solve a poly(d) sized problem instead. In practice, the best performances are often obtained by invoking these routines in an iterative fashion. We show these iterative methods can be adapted to give theoretical guarantees comparable and better than the current state of the art.

Our approaches are based on computing the importances of the rows, known as leverage scores, in an iterative manner. We show that alternating between computing a short matrix estimate and finding more accurate approximate leverage scores leads to a series of geometrically smaller instances. This gives an algorithm that runs in O(nnz(A)+d^{ω}∣^{+θ}ϵ^{-2}) time for any θ > 0, where the d^{ω}^{+θ} term is comparable to the cost of solving a regression problem on the small approximation. Our results are built upon the close connection between randomized matrix algorithms, iterative methods, and graph sparsification.

**FULL PAPER: pdf**