Related papers: Subexponential LPs Approximate Max-Cut

We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [RSW18]. Graph algorithms in this cut query model and other query models have recently been studied for various…

Trevisan [SICOMP 2012] presented an algorithm for Max-Cut based on spectral partitioning techniques. This is the first algorithm for Max-Cut with an approximation guarantee strictly larger than 1/2 that is not based on semidefinite…

We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut above the Edwards-Erd\H{o}s bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices…

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…

In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the `hard' instances of the Arora-Rao-Vazirani lemma [JACM'09], we show that the…

The log-density method is a powerful algorithmic framework which in recent years has given rise to the best-known approximations for a variety of problems, including Densest-$k$-Subgraph and Bipartite Small Set Vertex Expansion. These…

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…

In this paper, we present a polynomial-time algorithm that approximates sufficiently high-value Max 2-CSPs on sufficiently dense graphs to within $O(N^{\varepsilon})$ approximation ratio for any constant $\varepsilon > 0$. Using this…

We present a polynomial-time $(\alpha_{GW} + \varepsilon)$-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where $\alpha_{GW} \approx 0.878$ is the approximation guarantee of the Goemans-Williamson…

We consider the max-cut and max-$k$-cut problems under graph-based constraints. Our approach can handle any constraint specified using monadic second-order (MSO) logic on graphs of constant treewidth. We give a $\frac{1}{2}$-approximation…

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…

We propose an efficient $\epsilon$-differentially private algorithm, that given a simple {\em weighted} $n$-vertex, $m$-edge graph $G$ with a \emph{maximum unweighted} degree $\Delta(G) \leq n-1$, outputs a synthetic graph which…

We show a linear-size reduction from gap Max-2-Lin(2) (a generalization of the gap $\mathrm{Max}$-$\mathrm{Cut}$ problem) to $\gamma\text{-}\mathrm{CVP}_p$ for $\gamma = \mathrm{O}(1)$ and finite $p\geq 1$, as well as a no-go theorem…

Sublinear time algorithms for approximating maximum matching size have long been studied. Much of the progress over the last two decades on this problem has been on the algorithmic side. For instance, an algorithm of Behnezhad [FOCS'21]…

We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…

We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…

We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…

We study the applicability of distributed, local algorithms to 0/1 max-min LPs where the objective is to maximise ${\min_k \sum_v c_{kv} x_v}$ subject to ${\sum_v a_{iv} x_v \le 1}$ for each $i$ and ${x_v \ge 0}$ for each $v$. Here $c_{kv}…

Given a complete graph $G = (V, E)$ where each edge is labeled $+$ or $-$, the Correlation Clustering problem asks to partition $V$ into clusters to minimize the number of $+$edges between different clusters plus the number of $-$edges…

A longstanding open problem in coding theory is to determine the best (asymptotic) rate $R_2(\delta)$ of binary codes with minimum constant (relative) distance $\delta$. An existential lower bound was given by Gilbert and Varshamov in the…