Streaming Kernelization
Stefan Fafianie, Stefan Kratsch

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 bits of memory on instances . 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.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Parallel Computing and Optimization Techniques
