Streaming Verification of Graph Properties

TL;DR

This paper introduces efficient streaming interactive proofs capable of verifying maximum matchings exactly across various types and also provides the first streaming verification protocols for weighted matchings and metric TSP.

Contribution

It presents novel streaming interactive proof protocols for exact maximum matchings and the first for weighted matchings and metric TSP in streaming models.

Findings

Verified maximum matchings exactly in streaming settings.

Developed protocols for weighted matchings and metric TSP.

Achieved efficient verification with high probability.

Abstract

Streaming interactive proofs (SIPs) are a framework for outsourced computation. A computationally limited streaming client (the verifier) hands over a large data set to an untrusted server (the prover) in the cloud and the two parties run a protocol to confirm the correctness of result with high probability. SIPs are particularly interesting for problems that are hard to solve (or even approximate) well in a streaming setting. The most notable of these problems is finding maximum matchings, which has received intense interest in recent years but has strong lower bounds even for constant factor approximations. In this paper, we present efficient streaming interactive proofs that can verify maximum matchings exactly. Our results cover all flavors of matchings (bipartite/non-bipartite and weighted). In addition, we also present streaming verifiers for approximate metric TSP. In particular, these are the first efficient results for weighted matchings and for metric TSP in any streaming verification model.