Optimal Streaming Algorithms for Graph Matching
Jianer Chen, Qin Huang, Iyad Kanj, Ge Xia

TL;DR
This paper introduces new parameterized streaming algorithms for graph matching that operate efficiently in both dynamic and insert-only models, removing the need for prior knowledge of maximum matching size.
Contribution
It presents the first algorithms that do not require prior bounds on maximum matching size, achieving optimal space and update time complexities in streaming models.
Findings
Dynamic model algorithm computes maximum-weight k-matching in O(Wk^2) space
Insert-only model algorithm computes maximum-weight k-matching in O(k^2) space
Algorithms do not rely on prior bounds of maximum matching size
Abstract
We present parameterized streaming algorithms for the graph matching problem in both the dynamic and the insert-only models. For the dynamic streaming model, we present a one-pass algorithm that, with high probability, computes a maximum-weight -matching of a weighted graph in space and that has update time, where is the number of distinct edge weights and the notation hides a poly-logarithmic factor in the input size. For the insert-only streaming model, we present a one-pass algorithm that runs in space and has update time, and that, with high probability, computes a maximum-weight -matching of a weighted graph. The space complexity and the update-time complexity achieved by our algorithms for unweighted -matching in the dynamic model and for weighted -matching in the insert-only model are optimal. A…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Optimization and Search Problems · Distributed systems and fault tolerance
