Related papers: Graph cuts always find a global optimum for Potts …

In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems…

We consider the problem of finding a local optimum for Max-Cut with FLIP-neighborhood, in which exactly one node changes the partition. Schaeffer and Yannakakis (SICOMP, 1991) showed PLS-completeness of this problem on graphs with unbounded…

The main goal in distributed symmetry-breaking is to understand the locality of problems; i.e., the radius of the neighborhood that a node needs to explore in order to arrive at its part of a global solution. In this work, we study the…

We consider the massively parallel computation (MPC) model, which is a theoretical abstraction of large-scale parallel processing models such as MapReduce. In this model, assuming the widely believed 1-vs-2-cycles conjecture, solving many…

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both…

It has long been known that random regular graphs are with high probability good expanders. This was first established in the 1980s by Bollob\'as by directly calculating the probability that a set of vertices has small expansion and then…

A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…

In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…

We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum…

Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…

We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any…

We show that in random $K$-uniform hypergraphs of constant average degree, for even $K \geq 4$, local algorithms defined as factors of i.i.d. can not find nearly maximal cuts, when the average degree is sufficiently large. These algorithms…

We propose an algorithm for solving the time-dependent shortest path problem in flow fields where the FIFO (first-in-first-out) assumption is violated. This problem variant is important for autonomous vehicles in the ocean, for example,…

Given a training set, a loss function, and a neural network architecture, it is often taken for granted that optimal network parameters exist, and a common practice is to apply available optimization algorithms to search for them. In this…