Outsourced Computation Verification Roy Luo, UC Berkeley Under the mentorship of Graham Cormode, AT&T Labs DIMACS REU 2010

The Background Streaming Model Large amounts of data, limited memory E.g. Router observing network traffic Answer questions about data after only one pass E.g. what was the kth element? Most frequent element? One solution: outsource problem to a 3rd party with more computing power (cloud computing)

The Model You(verifier) and a 3rd party (helper) Both agents process entire data stream After seeing all the data, helper responds to verifier with answer to query Data Stream “Answer” V H

The Problem If we fully trust 3rd party, we’re done But: helper may have made an error or may be outright deceptive Require helper to prove correctness Need a “proof” that can be verified in limited space One-round model: H sends V one message containing the answer and a proof Multi-round model: H and V exchange messages until V is satisfied that H gave the right answer

An Example The INDEX problem: Without a helper, takes (N) space for N items (even probabilistically) Using one-round protocol, INDEX has solution with HV = O(Nlog(N)), H = length of helper’s message, V = space used by verifier E.g. H = O(√N), V = O(√N*log(N)) Using multi-round protocol, INDEX has a solution that uses V = O(log(N)) and H = O(log(N))

Directions for Research Are existing protocols practical for real-world use? What other problems require protocols? What class of problems can be solved in this model?