Optimal Per-Edge Processing Times in the Semi-Streaming Model

TL;DR

This paper introduces semi-streaming algorithms with optimal per-edge processing times for fundamental graph problems, achieving constant time per edge and matching classical RAM model efficiencies.

Contribution

The paper presents the first semi-streaming algorithms with optimal constant per-edge processing times for key graph problems, surpassing previous methods.

Findings

Achieved O(1) per-edge processing time for connected components and bipartition.

Reduced per-edge processing times for k-vertex and k-edge connectivity to O(1).

Matched classical RAM model algorithm efficiencies in the semi-streaming setting.

Abstract

We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when dealing with massive graphs, forbids random access to the input and restricts the memory to O(n*polylog n) bits. Particularly, the formerly best per-edge processing times for finding the connected components and a bipartition are O(alpha(n)), for determining k-vertex and k-edge connectivity O(k^2n) and O(n*log n) respectively for any constant k and for computing a minimum spanning forest O(log n). All these time bounds we reduce to O(1). Every presented algorithm determines a solution asymptotically as fast as the best corresponding algorithm up to date in the classical RAM model, which therefore cannot convert the advantage of unlimited memory and random access into superior computing times for these problems.