Related papers: Separating MAX 2-AND, MAX DI-CUT and MAX CUT
The MAX BISECTION problem seeks a maximum-size cut that evenly divides the vertices of a given undirected graph. An open problem raised by Austrin, Benabbas, and Georgiou is whether MAX BISECTION can be approximated as well as MAX CUT,…
Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that the approximation ratio of the Goemans-Williamson algorithm is optimal assuming…
Recently Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the Max Bisection problem. We improve their algorithm to a 0.8776-approximation. As Max Bisection is hard to approximate within $\alpha_{GW} + \epsilon \approx…
Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem.…
We study the MaxCut problem for graphs $G=(V,E)$. The problem is NP-hard, there are two main approximation algorithms with theoretical guarantees: (1) the Goemans \& Williamson algorithm uses semi-definite programming to provide a…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
MAX NAE-SAT is a natural optimization problem, closely related to its better-known relative MAX SAT. The approximability status of MAX NAE-SAT is almost completely understood if all clauses have the same size $k$, for some $k\ge 2$. We…
In the simultaneous Max-Cut problem, we are given $k$ weighted graphs on the same set of $n$ vertices, and the goal is to find a cut of the vertex set so that the minimum, over the $k$ graphs, of the cut value is as large as possible.…
Austrin showed that the approximation ratio $\beta\approx 0.94016567$ obtained by the MAX 2-SAT approximation algorithm of Lewin, Livnat and Zwick (LLZ) is optimal modulo the Unique Games Conjecture (UGC) and modulo a Simplicity Conjecture…
We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…
Max-Cut is a classical graph-partitioning problem where given a graph $G = (V,E)$, the objective is to find a cut $(S,S^c)$ which maximizes the number of edges crossing the cut. In a seminal work, Goemans and Williamson gave an $\alpha_{GW}…
The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…
In a second seminal paper on the application of semidefinite programming to graph partitioning problems, Goemans and Williamson showed how to formulate and round a complex semidefinite program to give what is to date still the best-known…
Exact solution of hard combinatorial optimization problems often relies on strong convex relaxations, but solving these relaxations repeatedly inside a branch-and-bound algorithm can be prohibitively expensive. Hence, we consider this…
We consider the question of approximating Max 2-CSP where each variable appears in at most $d$ constraints (but with possibly arbitrarily large alphabet). There is a simple $(\frac{d+1}{2})$-approximation algorithm for the problem. We prove…
In this note, we describe a $\alpha_{GW} + \tilde{\Omega}(1/d^2)$-factor approximation algorithm for Max-Cut on weighted graphs of degree $\leq d$. Here, $\alpha_{GW}\approx 0.878$ is the worst-case approximation ratio of the…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We study variants of the classic $s$-$t$ cut problem and prove the following improved hardness results assuming the Unique Games Conjecture (UGC). - For any constant $k \geq 2$ and $\epsilon > 0$, we show that Directed Multicut with $k$…
We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…
We study the Max-Cut semidefinite programming (SDP) relaxation in the regime where a near-optimal solution admits a low-dimensional realization. While the Goemans--Williamson hyperplane rounding achieves the worst-case optimal approximation…