相关论文: Vertex Nomination, Consistent Estimation, and Adve…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…

Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem…

Network interdiction problems are combinatorial optimization problems involving two players: one aims to solve an optimization problem on a network, while the other seeks to modify the network to thwart the first player's objectives. Such…

Given a set V of n elements on m attributes, we want to find a partition of V on the minimum number of clusters such that the associated R-squared ratio is at least a given threshold. We denote this problem as Goal Clustering (GC). This…

A set $D\subseteq V$ of a graph $G=(V,E)$ is called a restrained dominating set of $G$ if every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$. The \textsc{Minimum Restrained Domination} problem is to…

Popular matchings provide a model of matching under preferences in which a solution corresponds to a Condorcet winner in voting systems. In a bipartite graph in which the vertices have preferences over their neighbours, a matching is…

The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given simple graph $G=(V,E)$, a dominating set of $G$ is a subset $S\subseteq V$ such that every vertex in $…

Graph coloring is a fundamental problem in combinatorics with many applications in practice. In this problem, the vertices in a given graph must be colored by using the least number of colors in such a way that a vertex has a different…

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim…

Graph neural networks (GNNs) have struggled to outperform traditional optimization methods on combinatorial problems, limiting their practical impact. We address this gap by introducing a novel chaining procedure for the graph alignment…

It is now a standard for neural network representations to be trained on large, publicly available datasets, and used for new problems. The reasons for why neural network representations have been so successful for transfer, however, are…

Virtual Network Embedding (VNE) is a fundamental resource allocation challenge that is associated with hard and multifaceted constraints in network function virtualization (NFV). Existing works for VNE struggle to handle such complex…

Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…

We show that there exists an adjacency labelling scheme for planar graphs where each vertex of an $n$-vertex planar graph $G$ is assigned a $(1+o(1))\log_2 n$-bit label and the labels of two vertices $u$ and $v$ are sufficient to determine…

While message passing neural networks (MPNNs) have convincing success in a range of applications, they exhibit limitations such as the oversquashing problem and their inability to capture long-range interactions. Augmenting MPNNs with a…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…

Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and…

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…