Approximation Algorithms for Large Scale Data Analysis

Abstract

One of the greatest successes of computational complexity theory is the classification of countless fundamental computational problems into polynomial-time and NP-hard ones, two classes that are often referred to as tractable and intractable, respectively. However, this crude distinction of algorithmic efficiency is clearly insufficient when handling today's large scale of data. We need a finer-grained design and analysis of algorithms that pinpoints the exact exponent of polynomial running time, and a better understanding of when a speed-up is not possible. Based on stronger complexity assumptions than P vs NP, like the Strong Exponential Time Hypothesis, recently conditional lower bounds for a variety of fundamental problems in P have been proposed. Unfortunately, these conditional lower bounds often break down when one may settle for a near-optimal solution. Indeed, approximation algorithms can play a significant role when designing fast algorithms not just for traditional NP Hard problems, but also for polynomial time problems. For some applications arising in machine learning, the time complexity of the underlying algorithms is not sufficient to ensure a fast solution. It is often needed to collect side information about the data to ensure high accuracy. This requires low query complexity. In this presentation, we will cover new facets of fast algorithm design for large scale data analysis that emphasizes on the role of developing approximation algorithms for better polynomial time/query complexity.