Related papers: Efficient Dynamic Approximate Distance Oracles for…
There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures…
In 2001 Thorup and Zwick devised a distance oracle, which given an $n$-vertex undirected graph and a parameter $k$, has size $O(k n^{1+1/k})$. Upon a query $(u,v)$ their oracle constructs a $(2k-1)$-approximate path $\Pi$ between $u$ and…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
A comparison-based search algorithm lets a user find a target item $t$ in a database by answering queries of the form, ``Which of items $i$ and $j$ is closer to $t$?'' Instead of formulating an explicit query (such as one or several…
We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to…
The \emph{distance-number} of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the…
We investigate active learning with access to two distinct oracles: Label (which is standard) and Search (which is not). The Search oracle models the situation where a human searches a database to seed or counterexample an existing…
The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the…
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve…
An $L(2, 1)$-labeling of a graph $G$ is an assignment of a nonnegative integer to each vertex of $G$ such that adjacent vertices receive integers that differ by at least two and vertices at distance two receive distinct integers. The span…
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive…
We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of…
Existing visual tracking methods usually localize a target object with a bounding box, in which the performance of the foreground object trackers or detectors is often affected by the inclusion of background clutter. To handle this problem,…
Some properties of chaotic dynamical systems can be probed through features of recurrences, also called analogs. In practice, analogs are nearest neighbours of the state of a system, taken from a large database called the catalog. Analogs…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
Distance labeling schemes are schemes that label the vertices of a graph with short labels in such a way that the distance between any two vertices $u$ and $v$ can be determined efficiently by merely inspecting the labels of $u$ and $v$,…
We show how to preprocess a weighted undirected $n$-vertex planar graph in $\tilde O(n^{4/3})$ time, such that the distance between any pair of vertices can then be reported in $\tilde O(1)$ time. This improves the previous $\tilde…
Let $\ell$ denote a positive integer. A connected graph $\G$ of diameter at least $\ell$ is said to be $\ell${\it -distance-balanced} whenever for any pair of vertices $u,v$ of $\G$ such that $d(u,v)=\ell$, the number of vertices closer to…
Agreement protocols are crucial in various emerging applications, spanning from distributed (blockchains) oracles to fault-tolerant cyber-physical systems. In scenarios where sensor/oracle nodes measure a common source, maintaining output…
The evolving data framework was first proposed by Anagnostopoulos et al., where an evolver makes small changes to a structure behind the scenes. Instead of taking a single input and producing a single output, an algorithm judiciously probes…