Related papers: Graph-Based Nearest-Neighbor Search without the Sp…
$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially…
Graph neural networks (GNNs) can process graphs of different sizes, but their ability to generalize across sizes, specifically from small to large graphs, is still not well understood. In this paper, we identify an important type of data…
The explosive growth in big data has attracted much attention in designing efficient indexing and search methods recently. In many critical applications such as large-scale search and pattern matching, finding the nearest neighbors to a…
We present a geometric framework for filtered approximate nearest neighbor (ANN) search. Filtering a proximity graph by a metadata predicate produces a subgraph, a fiber, whose connectivity and geometry can differ sharply from the full…
We show how to represent a planar digraph in linear space so that distance queries can be answered in constant time. The data structure can be constructed in linear time. This representation of reachability is thus optimal in both time and…
Top-k Nearest Neighbors (kNN) problem on road network has numerous applications on location-based services. As direct search using the Dijkstra's algorithm results in a large search space, a plethora of complex-index-based approaches have…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree…
We study spectral algorithms for the high-dimensional Nearest Neighbor Search problem (NNS). In particular, we consider a semi-random setting where a dataset $P$ in $\mathbb{R}^d$ is chosen arbitrarily from an unknown subspace of low…
We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension, while the data is high-dimensional. We show that this problem can be solved…
In the model of \emph{local computation algorithms} (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space…
Nearest neighbor search has found numerous applications in machine learning, data mining and massive data processing systems. The past few years have witnessed the popularity of the graph-based nearest neighbor search paradigm because of…
Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…
Graph-based approximate nearest neighbor search has attracted more and more attentions due to its online search advantages. Numbers of methods studying the enhancement of speed and recall have been put forward. However, few of them focus on…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an $n$-point data set in a $d$-dimensional space our data structure achieves query time $O(d n^{\rho+o(1)})$ and space $O(n^{1+\rho+o(1)} +…
Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode…
Graph neural networks (GNNs) have been widely used in graph-related contexts. It is known that the separation power of GNNs is equivalent to that of the Weisfeiler-Lehman (WL) test; hence, GNNs are imperfect at identifying all…
Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing the information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly,…
Nearest Neighbor Search (NNS) has recently drawn a rapid increase of interest due to its core role in managing high-dimensional vector data in data science and AI applications. The interest is fueled by the success of neural embedding,…