Related papers: Generalized Metric Repair on Graphs
In the Directed Disjoint Paths problem, we are given a digraph $D$ and a set of requests $\{(s_1, t_1), \ldots, (s_k, t_k)\}$, and the task is to find a collection of pairwise vertex-disjoint paths $\{P_1, \ldots, P_k\}$ such that each…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct metric spaces. They are particularly useful in areas such as…
Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We…
The NP-hard Metric Dimension problem is to decide for a given graph G and a positive integer k whether there is a vertex subset of size at most k that separates all vertex pairs in G. Herein, a vertex v separates a pair {u,w} if the…
We present an additive $\varepsilon n^{2}$-approximation algorithm for the Graph Edit Distance problem (GED) on graphs of VC dimension $d$ running in time $n^{O(d/\varepsilon^{2})}$. In particular, this recovers a previous result by Arora,…
We have devised a simple numerical technique to treat rugged data points that arise due to the insufficient gain setting error (or quantization error) of a digital instrument. This is a very wide spread problem that all experimentalists…
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
For a family of graphs $\cal F$, the canonical Weighted $\cal F$ Vertex Deletion problem is defined as follows: given an $n$-vertex undirected graph $G$ and a weight function $w: V(G)\rightarrow\mathbb{R}$, find a minimum weight subset…
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also…
The article deals with the issue of modification of metric classification algorithms. In particular, it studies the algorithm k-Nearest Neighbours for its application to sequential data. A method of generalization of metric classification…
In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Data quality is paramount in today's data-driven world, especially in the era of generative AI. Dirty data with errors and inconsistencies usually leads to flawed insights, unreliable decision-making, and biased or low-quality outputs from…