Related papers: Graph Alignment via Birkhoff Relaxation
We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…
The symmetry of complex networks is a global property that has recently gained attention since MacArthur et al. 2008 showed that many real-world networks contain a considerable number of symmetries. These authors work with a very strict…
We study the classical weighted perfect matchings problem for bipartite graphs or sometimes referred to as the assignment problem, i.e., given a weighted bipartite graph $G = (U\cup V,E)$ with weights $w : E \rightarrow \mathcal{R}$ we are…
A graph $G(V, E)$ is \emph{claw-free} if no vertex has three pairwise non-adjacent neighbours. The Maximum Weight Stable Set (MWSS) Problem in a claw-free graph is a natural generalization of the Matching Problem and has been shown to be…
We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…
The Quadratic Assignment Problem (QAP) is an NP-hard fundamental combinatorial optimization problem introduced by Koopmans and Beckmann in 1957. The problem is to assign $n$ facilities to $n$ different locations with the goal of minimizing…
The Graphical House Allocation problem asks: how can $n$ houses (each with a fixed non-negative value) be assigned to the vertices of an undirected graph $G$, so as to minimize the "aggregate local envy", i.e., the sum of absolute…
We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational…
It has long been known, since the classical work of (Arora, Karger, Karpinski, JCSS~99), that \MC\ admits a PTAS on dense graphs, and more generally, \kCSP\ admits a PTAS on "dense" instances with $\Omega(n^k)$ constraints. In this paper we…
In the $0$-Extension problem, we are given an edge-weighted graph $G=(V,E,c)$, a set $T\subseteq V$ of its vertices called terminals, and a semi-metric $D$ over $T$, and the goal is to find an assignment $f$ of each non-terminal vertex to a…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…
The Tree Augmentation Problem (TAP) is a fundamental network design problem in which we are given a tree and a set of additional edges, also called \emph{links}. The task is to find a set of links, of minimum size, whose addition to the…
Given a set of vertices $V$ with $|V| = n$, a weight vector $w \in (\mathbb{R}^+ \cup \{ 0 \})^{\binom{V}{2}}$, and a probability vector $x \in [0, 1]^{\binom{V}{2}}$ in the matching polytope, we study the quantity $\frac{E_{G}[…
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and…
Given a pair of graphs $\textbf{A}$ and $\textbf{B}$, the problems of deciding whether there exists either a homomorphism or an isomorphism from $\textbf{A}$ to $\textbf{B}$ have received a lot of attention. While graph homomorphism is…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
Maximum A posteriori Probability (MAP) inference in graphical models amounts to solving a graph-structured combinatorial optimization problem. Popular inference algorithms such as belief propagation (BP) and generalized belief propagation…
Database alignment is a variant of the graph alignment problem: Given a pair of anonymized databases containing separate yet correlated features for a set of users, the problem is to identify the correspondence between the features and…