Related papers: Approximate Dynamic Nearest Neighbor Searching in …
Large-scale approximate nearest neighbor search (ANN) has been gaining attention along with the latest machine learning researches employing ANNs. If the data is too large to fit in memory, it is necessary to search for the most similar…
Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points $S$ and a radius parameter $r>0$, the $r$-near neighbor ($r$-NN) problem asks for a data structure that, given…
We consider the problem of designing a succinct data structure for {\it path graphs} (which are a proper subclass of chordal graphs and a proper superclass of interval graphs) on $n$ vertices while supporting degree, adjacency, and…
We present the first polynomial time approximation algorithm for computing shortest paths in weighted three-dimensional domains. Given a polyhedral domain $\D$, consisting of $n$ tetrahedra with positive weights, and a real number…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed epsilon > 0, we present a (1+epsilon)-approximate distance oracle with O(n(loglog n)^2) space and O((loglog n)^3) query time. This…
Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and O(n) space that can compute the…
Finding nearly accurate distance between two or more nearly intersecting three-dimensional (3D) objects is vital especially for collision determination such as in virtual surgeon simulation and real-time car crash simulation. Instead of…
Approximate nearest neighbor (ANN) search in high-dimensional spaces is a foundational component of many modern retrieval and recommendation systems. Currently, almost all algorithms follow an $\epsilon$-Recall-Bounded principle when…
k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic…
We consider data structures for graphs where we maintain a subset of the nodes called sites, and allow proximity queries, such as asking for the closest site to a query node, and update operations that enable or disable nodes as sites. We…
Given a set of $n$ sites from $\mathbb{R}^d$, each having some positive weight factor, the Multiplicatively Weighted Voronoi Diagram is a subdivision of space that associates each cell to the site whose weighted Euclidean distance is…
We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…
Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…
Given a polygon representing a transportation network together with a point p in its interior, we aim to extend the network by inserting a line segment, called a feed-link, which connects p to the boundary of the polygon. Once a feed link…
Approximate nearest neighbor search (ANNS) in high-dimensional spaces is a pivotal challenge in the field of machine learning. In recent years, graph-based methods have emerged as the superior approach to ANNS, establishing a new state of…
We study the problem of computing Chamfer distance in the fully dynamic setting, where two set of points $A, B \subset \mathbb{R}^{d}$, each of size up to $n$, dynamically evolve through point insertions or deletions and the goal is to…
In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…
Range closest-pair (RCP) search is a range-search variant of the classical closest-pair problem, which aims to store a given set $S$ of points into some space-efficient data structure such that when a query range $Q$ is specified, the…