Lower Bounds for Multi-Pass Processing of Multiple Data Streams

TL;DR

This paper introduces a new multi-pass automaton model for processing multiple data streams, presents algorithms for set disjointness, and establishes lower bounds on memory and head requirements for this problem.

Contribution

It proposes the mp2s-automata model, provides algorithms for set disjointness, and proves fundamental lower bounds on resources needed for this task.

Findings

Algorithms for set disjointness using mp2s-automata

Lower bounds on memory size for set disjointness

Lower bounds on number of heads required for set disjointness

Abstract

This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called mp2s-automata. Two algorithms for solving the set disjointness problem wi th these automata are presented. The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solvin g the set disjointness problem with mp2s-automata.