Related papers: The Extraction and Complexity Limits of Graphical …
Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a…
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
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…
Designing molecules with specific properties is a long-lasting research problem and is central to advancing crucial domains such as drug discovery and material science. Recent advances in deep graph generative models treat molecule design…
We propose an algebraic geometric framework to study the expressivity of linear activation neural networks. A particular quantity of neural networks that has been actively studied is the number of linear regions, which gives a…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In…
Established methods for structural elicitation typically rely on code modelling standard graphical models classes, most often Bayesian networks. However, more appropriate models may arise from asking the expert questions in common language…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to…
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form,…