# Large-scale optimization

Our mission is to develop large-scale optimization techniques and use them to improve the efficiency and robustness of infrastructure at Google.

# Large-scale optimization

Our mission is to develop large-scale optimization techniques and use them to improve the efficiency and robustness of infrastructure at Google.

## Background

We apply techniques from areas such as combinatorial optimization, online algorithms, and control theory to make Google’s big computational infrastructure do more with less. We combine online and offline optimizations to achieve such goals as increasing throughput, decreasing latency, minimizing resource contention, maximizing the efficacy of caches, and eliminating unnecessary work in distributed systems. Our research is used in critical infrastructure that supports products such as Search and Cloud.

## Some of our projects

We design memoryless balanced allocation algorithms to assign a dynamic set of tasks to a dynamic set of servers such that the load (the number of assigned tasks) on each server is bounded, and the allocation does not change by much for every update operation.

Composable core-sets provide an effective method for solving optimization problems on massive datasets. The main idea is to partition data among some number of machines, then use each machine to compute some small summary/sketch of the data. After gathering all summaries on one machine, we solve the original optimization problem.

Maximum coverage and minimum set-cover problems are among the fundamental problems in combinatorial optimization and have a variety of applications in machine learning and data mining. We study these problems in the streaming and MapReduce models of computation, and develop practical algorithms with tight theoretical bounds for runtime, space and approximation guarantee. Our main idea is a novel sketching technique that compresses the input into a small space, independent of the size of the ground set, without hurting the quality by much.

Several of our projects have partnered with product teams to help improve the efficiency of Google's search infrastructure. In the backend for web search, we introduced a distributed feedback control loop to govern the way queries are fanned out to worker machines, in order to balance load better by taking advantage of real-time load information on the workers. We also improved the efficacy of caching by increasing the homogeneity of the stream of queries seen by any single worker machine. To accomplish this, we clustered query terms, used these clusters to define voting weights, and assigned queries to workers on the basis of votes cast by the terms in the query. In a pub-sub system that powers some of our display ads, we saved computation by clustering some components of subscriptions in a way that lets us take advantage of bitwise-parallel CPU operations.