Related papers: Efficient Construction of Neighborhood Graphs by t…
Proximity graphs (PG) have gained increasing popularity as the state-of-the-art solutions to $k$-approximate nearest neighbor ($k$-ANN) search on high-dimensional data, which serves as a fundamental function in various fields, e.g.,…
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
A graph G'(V,E') is an \eps-sparsification of G for some \eps>0, if every (weighted) cut in G' is within (1\pm \eps) of the corresponding cut in G. A celebrated result of Benczur and Karger shows that for every undirected graph G, an…
Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…
Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…
Pandemic measures such as social distancing and contact tracing can be enhanced by rapidly integrating dynamic location data and demographic data. Projecting billions of longitude and latitude locations onto hundreds of thousands of highly…
Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…
Range-filtering approximate nearest neighbor (RFANN) search is attracting increasing attention in academia and industry. Given a set of data objects, each being a pair of a high-dimensional vector and a numeric value, an RFANN query with a…
Network Diversion is a graph problem that has been extensively studied in both the network-analysis and operations-research communities as a measure of how robust a network is against adversarial disruption. This problem is especially well…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…
We are interested in the problem of finding $k$ nearest neighbours in the plane and in the presence of polygonal obstacles ($\textit{OkNN}$). Widely used algorithms for OkNN are based on incremental visibility graphs, which means they…
We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to…
Local search is a fundamental method in operations research and combinatorial optimisation. It has been widely applied to a variety of challenging problems, including multi-objective optimisation where multiple, often conflicting,…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…
We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.…
$\renewcommand{\Re}{\mathbb{R}}$Given a set $P$ of $n$ points in $\Re^d$, and a parameter $\varepsilon \in (0,1)$, we present a new construction of a directed graph $G$, of size $O(n/\varepsilon^d)$, such that $(1+\varepsilon)$-ANN queries…
Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…