Related papers: Heuristic Algorithms for Best Match Graph Editing
Spectral algorithms are an important building block in machine learning and graph algorithms. We are interested in studying when such algorithms can be applied directly to provide optimal solutions to inference tasks. Previous works by…
Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g.\ in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of determining a minimum-cost elimination ordering, which we call…
We give a combinatorial condition for the existence of efficient, LP-based FPT algorithms for a broad class of graph-theoretical optimisation problems. Our condition is based on the notion of biased graphs known from matroid theory.…
In this work, we study the cost efficient data versioning problem, where the goal is to optimize the storage and reconstruction (retrieval) costs of data versions, given a graph of datasets as nodes and edges capturing edit/delta…
Molecular machine learning has gained popularity with the advancements of geometric deep learning. In parallel, retrieval-augmented generation has become a principled approach commonly used with language models. However, the optimal…
Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for…
Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a…
Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM).…
Bipartite best match graphs (BMG) and their generalizations arise in mathematical phylogenetics as combinatorial models describing evolutionary relationships among related genes in a pair of species. In this work, we characterize the class…
Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…
We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the…
Subgraph matching is a NP-complete problem that extracts isomorphic embeddings of a query graph $q$ in a data graph $G$. In this paper, we present a framework with three components: Preprocessing, Reordering and Enumeration. While pruning…
A $b$-coloring of a graph is a proper vertex coloring such that each color class contains a vertex that sees all other colors in its neighborhood. The $b$-coloring problem, in which the task is to decide whether a graph admits a…
Individual's semantics have been used for guiding the learning process of Genetic Programming solving supervised learning problems. The semantics has been used to proposed novel genetic operators as well as different ways of performing…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
Many statistical problems involve optimization over a discrete parameter space having an unknown dimension. In such settings, gradient-based methods often fail due to the non-differentiability of the objective function or a non-convex or…