---
author:
- 'Sepehr Abbasi-Zadeh [^1]'
- 'Nikhil Bansal[^2]'
- 'Guru Guruganesh [^3]'
- 'Aleksandar Nikolov [^4]'
- 'Roy Schwartz [^5]'
- 'Mohit Singh [^6]'
bibliography:
- 'main.bib'
title: Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems
---

Brownian Rounding for [<span style="font-variant:small-caps;">Max-Cut</span>]{}via Conformal Mappings {#sec:conformal}
=====================================================================================================

Brownian Rounding for [<span style="font-variant:small-caps;">Max-2SAT</span>]{}via Partial Differential Equations {#sec:pde}
==================================================================================================================

[<span style="font-variant:small-caps;">Max-Cut</span>]{}with Side Constraints ([<span style="font-variant:small-caps;">Max-Cut-SC</span>]{}) {#sect:mc-constraints}
=============================================================================================================================================

Extensions of the Brownian Rounding {#sec:general}
===================================

Acknowledgements
================

The authors are grateful to Assaf Naor and Ronen Eldan for sharing their manuscript with us.  SA would like to thank Gantumur Tsogtgerel for bringing the Maximum Principle to our attention, and Christina C. Christara for helping us compare various numerical PDE solvers.  SA and AN thank Allan Borodin for useful discussions during the initial stages of this research.  GG would like to thank Anupam Gupta and Ian Tice for useful discussion, and for also pointing out the Maximum Principle. 

SA and AN were supported by an NSERC Discovery Grant (RGPIN-2016-06333).  MS was supported by NSF grant CCF-BSF:AF1717947.  Some of this work was carried out while AN and NB were visitors at the Simons Institute program on Bridging Discrete and Continuous Optimization, partially supported by NSF grant \#CCF-1740425. 

[^1]: University of Toronto.  E-mail: `sabbasizadeh@gmail.com`. 

[^2]: TU Eindhoven, and Centrum Wiskunde & Informatica.  E-mail: `bansal@gmail.com`. 

[^3]: Google Research.  Email: `gurug@google.com`. 

[^4]: University of Toronto.  Email:`anikolov@cs.toronto.edu`. 

[^5]: Technion.  Email:`schwartz@cs.technion.ac.il`. 

[^6]: Georgia Institute of Technology.  Email:`mohitsinghr@gmail.com`.