Related papers: New Best-Known Max-Cut Solution for the G63 Instan…

We present a batch trajectory optimizer that can simultaneously solve hundreds of different instances of the problem in real-time. We consider holonomic robots but relax the assumption of circular base footprint. Our main algorithmic…

One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every…

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and…

This work addresses the task of instance-aware semantic segmentation. Our key motivation is to design a simple method with a new modelling-paradigm, which therefore has a different trade-off between advantages and disadvantages compared to…

We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our…

We consider network-based decentralized optimization problems, where each node in the network possesses a local function and the objective is to collectively attain a consensus solution that minimizes the sum of all the local functions. A…

The maximum clique problem, a well-known graph-based combinatorial optimization problem, has been addressed through various algorithmic approaches, though systematic analyses of the problem instances remain sparse. This study employs the…

We consider the Max-Cut problem. Let $G = (V,E)$ be a graph with adjacency matrix $(a_{ij})_{i,j=1}^{n}$. Burer, Monteiro & Zhang proposed to find, for $n$ angles $\left\{\theta_1, \theta_2, \dots, \theta_n\right\} \subset [0, 2\pi]$,…

Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph $G=(V, E)$ whose edges $E$ have unknown capacity values that are to be…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…

This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Networks (GNNs) -- a class of neural networks designed to learn…

Autonomous robots require efficient on-device learning to adapt to new environments without cloud dependency. For this edge training, Microscaling (MX) data types offer a promising solution by combining integer and floating-point…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

We consider the following stochastic optimization problem first introduced by Chen et al. in \cite{chen}. We are given a vertex set of a random graph where each possible edge is present with probability p_e. We do not know which edges are…

The graph partitioning problem (GPP) is among the most challenging models in optimization. Because of its NP-hardness, the researchers directed their interest towards approximate methods such as the genetic algorithms (GA). The edge-based…

We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…

We introduce a GPU-accelerated Monte Carlo framework for nonconvex, free-final-time trajectory optimization problems. This framework makes use of the prox-linear method, which belongs to the larger family of sequential convex programming…

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…