The Sparse Awakens: Streaming Algorithms for Matching Size Estimation in Sparse Graphs
Graham Cormode, Hossein Jowhari, Morteza Monemizadeh, S., Muthukrishnan

TL;DR
This paper introduces new streaming algorithms for estimating maximum matching size in sparse graphs, significantly improving space complexity and leveraging streaming order and structural properties.
Contribution
It presents the first one-pass streaming algorithms for maximum matching size estimation in sparse graphs with improved space bounds for both insert-only and dynamic streams.
Findings
One-pass algorithm for insert-only streams with O(c log^2 n) space.
One-pass algorithm for dynamic streams with O~(c^{10/3} n^{2/3}) space.
Improved approximation factors for maximum matching in sparse graphs.
Abstract
Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating the size of maximum matching with sparse (bounded arboricity) graphs. * Insert-Only Streams: We present a one-pass algorithm that takes O(c log^2 n) space and approximates the size of the maximum matching in graphs with arboricity c within a factor of O(c). This improves significantly on the state-of-the-art O~(cn^{2/3})-space streaming algorithms. * Dynamic Streams: Given a dynamic graph stream (i.e., inserts and deletes) of edges of an underlying c-bounded arboricity graph, we present a one-pass algorithm that uses space O~(c^{10/3}n^{2/3}) and returns an O(c)-estimator for the size of the maximum matching. This algorithm improves the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
