Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition

TL;DR

This paper advances the understanding of communication complexity and stream computation by establishing new bounds for augmented index problems, resolving open questions on language recognition complexity, and introducing passive memory checkers for data structures.

Contribution

It provides the first bounds on information complexity for augmented index, solves an open problem on Dyck language recognition, and develops passive memory checkers for various data structures.

Findings

New bounds on information complexity of AUGMENTED-INDEX.

Separation between multi-pass and multi-pass with reverse passes.

First passive memory checkers for priority queues, stacks, and deques.

Abstract

This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of AUGMENTED-INDEX. In contrast to analogous results for INDEX by Jain, Radhakrishnan and Sen [J. ACM, 2009], we have to overcome the significant technical challenge that protocols for AUGMENTED-INDEX may violate the "rectangle property" due to the inherent input sharing. Second, we use these bounds to resolve an open problem of Magniez, Mathieu and Nayak [STOC, 2010] that asked about the multi-pass complexity of recognizing Dyck languages. This results in a natural separation between the standard multi-pass model and the multi-pass model that permits reverse passes. Third, we present the first passive memory checkers that verify the interaction transcripts of priority queues, stacks, and double-ended queues. We obtain tight upper and lower bounds for these problems, thereby addressing an important sub-class of the memory checking framework of Blum et al. [Algorithmica, 1994].