Related papers: New Best-Known Max-Cut Solution for the G63 Instan…
A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been…
We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-$k$-ECSS problem, we are given a graph $G=(V,E)$ whose edges have non-negative…
MaxCut is a classical NP-complete problem and a crucial building block in many combinatorial algorithms. The famous Edwards-Erd\H{o}s bound states that any connected graph on n vertices with m edges contains a cut of size at least $m/2 +…
Wepropose SplitGNN, a graph neural network (GNN)-based approach that learns to solve weighted maximum satisfiabil ity (MaxSAT) problem. SplitGNN incorporates a co-training architecture consisting of supervised message passing mech anism and…
Handling clustering problems are important in data statistics, pattern recognition and image processing. The mean-shift algorithm, a common unsupervised algorithms, is widely used to solve clustering problems. However, the mean-shift…
We consider the Max-$3$-Section problem, where we are given an undirected graph $ G=(V,E)$ equipped with non-negative edge weights $w :E\rightarrow \mathbb{R}_+$ and the goal is to find a partition of $V$ into three equisized parts while…
The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to…
In the Coloured Clustering problem, we wish to colour vertices of an edge coloured graph to produce as many stable edges as possible, i.e., edges with the same colour as their ends. In this paper, we reveal that the problem is in fact a…
The performance of graph programs depends highly on the algorithm, the size and structure of the input graphs, as well as the features of the underlying hardware. No single set of optimizations or one hardware platform works well across all…
In this article, we continue our analysis for a novel recursive modification to the Max $k$-Cut algorithm using semidefinite programming as its basis, offering an improved performance in vectorized data clustering tasks. Using a dimension…
In a recent breakthrough, Zhang proves that if $G$ is an $H$-free graph with $m$ edges, then $G$ has a cut of size at least $m/2+c_Hm^{0.5001}$, making a significant step towards a well known conjecture of Alon, Bollob\'as, Krivelevich and…
Correlation clustering is a fundamental combinatorial optimization problem arising in many contexts and applications that has been the subject of dozens of papers in the literature. In this problem we are given a general weighted graph…
Baader, J\"org, and Parlier recently established an upper bound for the crossing number of curve systems of size $m\asymp g^{1+\alpha}$ on a genus $g$ surface, obtaining a leading coefficient of $9/4=2.25$. Their construction relies on…
Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…
In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices…
We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental…
Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…
We implement exact triangle counting in graphs on the GPU using three different methodologies: subgraph matching to a triangle pattern; programmable graph analytics, with a set-intersection approach; and a matrix formulation based on sparse…
We give an approximation algorithm for MaxCut and provide guarantees on the average fraction of edges cut on $d$-regular graphs of girth $\geq 2k$. For every $d \geq 3$ and $k \geq 4$, our approximation guarantees are better than those of…
We present MADAM, a parallel semidefinite based exact solver for Max-Cut, a problem of finding the cut with maximum weight in a given graph. The algorithm uses branch and bound paradigm that applies alternating direction method of…