# Deterministic Rounding of Dynamic Fractional Matchings

@inproceedings{Bhattacharya2021DeterministicRO, title={Deterministic Rounding of Dynamic Fractional Matchings}, author={Sayan Bhattacharya and P{\'e}ter Kiss}, booktitle={ICALP}, year={2021} }

We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first deterministic algorithm for maintaining a $(2-\delta)$-approximate maximum matching in a fully dynamic bipartite graph, in arbitrarily small polynomial update time. (2) The first deterministic algorithm for maintaining a $(1+\delta)$-approximate maximum matching in a…

## 14 Citations

Deterministic Dynamic Matching in Worst-Case Update Time

- Computer ScienceITCS
- 2022

We present deterministic algorithms for maintaining a (3/2 + ε) and (2 + ε)-approximate maximum matching in a fully dynamic graph with worst-case update times Ô( √ n) and Õ(1)1 respectively. The…

Beating the Folklore Algorithm for Dynamic Matching

- Computer ScienceITCS
- 2022

This work presents the first deterministic algorithm which outperforms the folklore algorithm in terms of both approximation ratio and worst-case update time, and shows how to use dynamic bipartite matching algorithms as black-box subroutines for dynamic matching in general graphs without incurring the natural 2 factor in the approximation ratio which such approaches naturally incur.

Dynamic Algorithms for Packing-Covering LPs via Multiplicative Weight Updates

- Mathematics, Computer ScienceArXiv
- 2022

This paper settles the complexity of dynamic packing and covering LPs, up to a polylogarithmic factor in update time, and initiates a systematic study of the multiplicative weights update (MWU) method in the dynamic setting.

Dynamic Algorithms for Maximum Matching Size

- Computer Science, MathematicsArXiv
- 2022

This paper shows that when the goal is to maintain just the size of the matching instead of its edge-set, then these bounds can indeed be improved.

Decremental Matching in General Graphs

- Mathematics, Computer ScienceICALP
- 2022

This paper bridges the gap between bipartite and general graphs, by giving an O ε (poly(log n )) update time algorithm that maintains a (1 + ε )-approximate maximum integral matching under adversarial deletions.

New Trade-Offs for Fully Dynamic Matching via Hierarchical EDCS

- Computer ScienceSODA
- 2022

A new approach to designing fully dynamic approximate matching algorithms that in a unified manner recovers all previously known trade-offs that were achieved via very different techniques, but reveals some new ones as well.

Maintaining an EDCS in General Graphs: Simpler, Density-Sensitive and with Worst-Case Time Bounds

- Computer Science, MathematicsSOSA
- 2022

This work simplifies the approach of Bernstein and Stein for bipartite graphs, which allows it to generalize it for general graphs while maintaining the same bound of O (m ) on the worst-case update time.

On Regularity Lemma and Barriers in Streaming and Dynamic Matching

- Mathematics, Computer ScienceArXiv
- 2022

This work presents a new approach for matchings in dense graphs by building on Szemer´edi’s celebrated Regularity Lemma, and presents a randomized (1 − o (1))-approximation algorithm whose space can be upper bounded by the density of certain Ruzsa-Szemer'edi (RS) graphs.

Simple Dynamic Spanners with Near-optimal Recourse against an Adaptive Adversary

- Computer Science, MathematicsArXiv
- 2022

This paper completely closes the gap with respect to recourse by showing algorithms against an adaptive adversary with near-optimal size-stretch trade-oﬀ and recourse and shows another algorithm that maintains a 3-spanner of size O ( n 1 . 5 ) with polylog( n ) amortized recourse and simultaneously O ( √ n ) worst-case update time.

Dynamic Matching with Better-than-2 Approximation in Polylogarithmic Update Time

- Computer ScienceArXiv
- 2022

The key new idea is to invoke the recent sublinear-time matching algorithm of Behnezhad in a white-box manner to simulate the second pass of the streaming algorithms, while bypassing the well-known vertex-update barrier.

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