Related papers: A Unified Framework for Integer Programming Formul…

It is a notorious open question whether integer programs (IPs), with an integer coefficient matrix $M$ whose subdeterminants are all bounded by a constant $\Delta$ in absolute value, can be solved in polynomial time. We answer this question…

Multigraph matching is a recent variant of the graph matching problem. In this framework, the optimization procedure considers several graphs and enforces the consistency of the matches along the graphs. This constraint can be formalized as…

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance.…

Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at…

Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of…

Big graph mining is an important research area and it has attracted considerable attention. It allows to process, analyze, and extract meaningful information from large amounts of graph data. Big graph mining has been highly motivated not…

Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

We propose a new graph-theoretic benchmark in this paper. The benchmark is developed to address shortcomings of an existing widely-used graph benchmark. We thoroughly studied a large number of traditional and contemporary graph algorithms…

This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…

Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…

Over the last decade, the vertex-centric programming model has attracted significant attention in the world of graph processing, resulting in the emergence of a number of vertex-centric frameworks. Its simple programming interface, where…

We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…

We investigate the computational complexity of problems on toric ideals such as normal forms, Gr\"obner bases, and Graver bases. We show that all these problems are strongly NP-hard in the general case. Nonetheless, we can derive efficient…

Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…

This paper is devoted to a study of single-peakedness on arbitrary graphs. Given a collection of preferences (rankings of a set of alternatives), we aim at determining a connected graph G on which the preferences are single-peaked, in the…

Graph Neural Networks (GNNs) have emerged as a prominent framework for graph mining, leading to significant advances across various domains. Stemmed from the node-wise representations of GNNs, existing explanation studies have embraced the…

Graph mining applications analyze the structural properties of large graphs, and they do so by finding subgraph isomorphisms, which makes them computationally intensive. Existing graph mining techniques including both custom graph mining…

Image matching is a key component of many tasks in computer vision and its main objective is to find correspondences between features extracted from different natural images. When images are represented as graphs, image matching boils down…