Related papers: Solving Unique Games over Globally Hypercontractiv…
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…
External knowledge graphs (KGs) can be used to augment large language models (LLMs), while simultaneously providing an explainable knowledge base of facts that can be inspected by a human. This approach may be particularly valuable in…
The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced…
In Clique Cover, given a graph $G$ and an integer $k$, the task is to partition the vertices of $G$ into $k$ cliques. Clique Cover on unit ball graphs has a natural interpretation as a clustering problem, where the objective function is the…
We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…
Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…
Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central…
Given a connected graph $G$ and its vertex $x$, let $U_x(G)$ denote the universal cover of $G$ obtained by unfolding $G$ into a tree starting from $x$. Let $T=T(n)$ be the minimum number such that, for graphs $G$ and $H$ with at most $n$…
Causal discovery aims to recover a causal graph from data generated by it; constraint based methods do so by searching for a d-separating conditioning set of nodes in the graph via an oracle. In this paper, we provide analytic evidence that…
We study unit ball graphs (and, more generally, so-called noisy uniform ball graphs) in $d$-dimensional hyperbolic space, which we denote by $\mathbb{H}^d$. Using a new separator theorem, we show that unit ball graphs in $\mathbb{H}^d$…
Graph neural networks have pushed state-of-the-arts in graph classifications recently. Typically, these methods are studied within the context of supervised end-to-end training, which necessities copious task-specific labels. However, in…
In this paper, we prove an almost-optimal hardness for Max $k$-CSP$_R$ based on Khot's Unique Games Conjecture (UGC). In Max $k$-CSP$_R$, we are given a set of predicates each of which depends on exactly $k$ variables. Each variable can…
Graph neural networks (GNNs) have emerged as a powerful tool for solving combinatorial optimization problems (COPs), exhibiting state-of-the-art performance in both graph-structured and non-graph-structured domains. However, existing…
We show how the discovery of robust scalable numerical solvers for arbitrary bounded linear operators can be automated as a Game Theory problem by reformulating the process of computing with partial information and limited resources as that…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Let $\mathcal{G}$ be a compact group and let $f_{ij} \in L^2(\mathcal{G})$. We define the Non-Unique Games (NUG) problem as finding $g_1,\dots,g_n \in \mathcal{G}$ to minimize $\sum_{i,j=1}^n f_{ij} \left( g_i g_j^{-1}\right)$. We devise a…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
Expander graphs play a central role in graph theory and algorithms. With a number of powerful algorithmic tools developed around them, such as the Cut-Matching game, expander pruning, expander decomposition, and algorithms for decremental…
Designing effective graph neural networks (GNNs) with message passing has two fundamental challenges, i.e., determining optimal message-passing pathways and designing local aggregators. Previous methods of designing optimal pathways are…