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A Note on Rounding Matchings in General Graphs

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arxiv 2402.03068 v1 pith:JJACAMVN submitted 2024-02-05 cs.DS

Aditi Dudeja This is my paper · ORCID
classification cs.DS
keywords algorithmroundingfractionalgeneralgraphsmatchingmatchingsnote
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abstract

In this note, we revisit the rounding algorithm of Wajc. Wajc gave a fully-adaptive randomized algorithm that rounds a dynamic fractional matching in an unweighted bipartite graph to an integral matching of nearly the same value in $O(\text{poly}(\log n,\frac{1}{\varepsilon}))$ update time. We give show that the guarantees of this algorithm hold for general graphs as well. Additionally, we show useful properties of this subroutine which have applications in rounding weighted fractional matchings.

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Cited by 1 Pith paper

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  1. Deterministic Dynamic Maximal Matching in Sublinear Update Time

    cs.DS 2025-04 accept novelty 8.0 of 10

    A fully dynamic maximal matching can be maintained deterministically in O~(n^(8/9)) amortized update time, the first sublinear deterministic bound.

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