相关论文: Distance Oracles for Interval Graphs via Breadth-F…

A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…

Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…

Low density graphs are considered to be a realistic graph class for modelling road networks. It has advantages over other popular graph classes for road networks, such as planar graphs, bounded highway dimension graphs, and spanners. We…

We consider the problem of finding small distance-preserving subgraphs of undirected, unweighted interval graphs with $k$ terminal vertices. To start with, we show that finding an optimal distance-preserving subgraph is $\mathsf{NP}$-hard…

We study point-to-point distance estimation in hypergraphs, where the query is parameterized by a positive integer s, which defines the required level of overlap for two hyperedges to be considered adjacent. To answer s-distance queries, we…

We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity $f$ for an FPT problem $\Pi$ on a graph $G$ with parameter $k$…

We present a labeling scheme that assigns labels of size $\tilde O(1)$ to the vertices of a directed weighted planar graph $G$, such that for any fixed $\varepsilon>0$ from the labels of any three vertices $s$, $t$ and $f$ one can determine…

We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…

(Directed) graphs with node attributes are a common type of data in various applications and there is a vast literature on developing metrics and efficient algorithms for comparing them. Recently, in the graph learning and optimization…

Metrics for merge trees that are simultaneously stable, informative, and efficiently computable have so far eluded researchers. We show in this work that it is possible to devise such a metric when restricting merge trees to ordered domains…

Le and Wulff-Nilsen [SODA '24] initiated a systematic study of VC set systems to unweighted $K_h$-minor-free directed graphs. We extend their results in the following ways: $\bullet$ We present the first application of VC set systems for…

The last in-tree recognition problem asks whether a given spanning tree can be derived by connecting each vertex with its rightmost left neighbor of some search ordering. In this study, we demonstrate that the last-in-tree recognition…

Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the…

Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…

Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…

We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…

Given a vertex-labeled graph, each vertex $v$ is attached with a label from a set of labels. The vertex-label query desires the length of the shortest path from the given vertex to the set of vertices with the given label. We show how to…

Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge…

With the growing focus on semantic searches and interpretations, an increasing number of standardized vocabularies and ontologies are being designed and used to describe data. We investigate the querying of objects described by a…

We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order…