Optimal Web-Scale Tiering as a Flow Problem

We present a fast online solver for large scale parametric max-flow problems as they occur in portfolio optimization, inventory management, computer vision, and logistics; •Our algorithm solves an integer linear program in an online fashion; • It exploits total unimodularity of the constraint matrix and a Lagrangian relaxation to solve the problem as a convex online game; • The algorithm generates approximate solutions of max-flow problems by performing stochastic gradient descent on a set of flows; •We apply the algorithm to optimize tier arrangement of over 80 Million web pages on a layered set of caches to serve an incoming query stream optimally. Motivating Example The Tiering Problem Goal: • Select documents to be stored in successive tiers or caches of decreasing access frequency • such that frequently accessed documents are found in the highest tiers • thus the search engine will be able to cover incoming queries with low latency and computational load. One proposed solution: •Assign a value to each document and arrange them such that the highest valued documents reside in the highest levels of the cache; • But this is sub-optimal. Reason: to answer a given query well, a search engine returns not only a single document but a list of r (typically r = 10) documents. doc 1 doc 2. doc 3 doc 4 doc 5 doc 6 doc 7 doc 8 doc 9 doc 10 cache 1