Streaming Kernelization

TL;DR

This paper introduces a streaming variant of kernelization for hard problems, analyzing how multiple passes over input data affect preprocessing efficiency and memory use, with Edge Dominating Set as a key example.

Contribution

It formalizes streaming kernelization, explores the impact of multiple passes, and provides bounds for problems like Edge Dominating Set.

Findings

Single-pass kernelization is not possible for Edge Dominating Set.

Two passes suffice to achieve standard kernelization bounds.

Streaming kernelization depends on the number of input passes.

Abstract

Kernelization is a formalization of preprocessing for combinatorially hard problems. We modify the standard definition for kernelization, which allows any polynomial-time algorithm for the preprocessing, by requiring instead that the preprocessing runs in a streaming setting and uses $\mathcal{O}(poly(k)\log|x|)$ bits of memory on instances $(x,k)$. We obtain several results in this new setting, depending on the number of passes over the input that such a streaming kernelization is allowed to make. Edge Dominating Set turns out as an interesting example because it has no single-pass kernelization but two passes over the input suffice to match the bounds of the best standard kernelization.