Related papers: Product Range Search Problem
In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…
We study the following problem that is motivated by demand-aware network design: Given a tree~$G$, the task is to find a binary tree~$H$ on the same vertex set. The objective is to minimize the sum of distances in~$H$ between vertex pairs…
Suppose we know that an object is in a sorted table and we want to determine the index of that object. To achieve this goal we could perform a binary search. However, suppose it is time-consuming to determine the relative position of that…
Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of…
This paper studies the $r$-range search problem for curves under the continuous Fr\'echet distance: given a dataset $S$ of $n$ polygonal curves and a threshold $r>0$, construct a data structure that, for any query curve $q$, efficiently…
Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range query and update operations. A Segment Tree divides the…
We revisit the classic problem of simplex range searching and related problems in computational geometry. We present a collection of new results which improve previous bounds by multiple logarithmic factors that were caused by the use of…
CAT(0) metric spaces constitute a far-reaching common generalization of Euclidean and hyperbolic spaces and simple polygons: any two points x and y of a CAT(0) metric space are connected by a unique shortest path {\gamma}(x,y). In this…
Retrieving points based on proximity in a high-dimensional vector space is a crucial step in information retrieval applications. The approximate nearest neighbor search (ANNS) problem, which identifies the $k$ nearest neighbors for a query,…
With the continued digitization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
Symbolic Regression tries to find a mathematical expression that describes the relationship of a set of explanatory variables to a measured variable. The main objective is to find a model that minimizes the error and, optionally, that also…
Given a dataset $S$ of points in $\mathbb{R}^2$, the range closest-pair (RCP) problem aims to preprocess $S$ into a data structure such that when a query range $X$ is specified, the closest-pair in $S \cap X$ can be reported efficiently.…
Despite the constant evolution of similarity searching research, it continues to face the same challenges stemming from the complexity of the data, such as the curse of dimensionality and computationally expensive distance functions.…
A mode of a multiset $S$ is an element $a \in S$ of maximum multiplicity; that is, $a$ occurs at least as frequently as any other element in $S$. Given a list $A[1:n]$ of $n$ items, we consider the problem of constructing a data structure…
Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms…
Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric…
Given the proximity of many wireless users and their diversity in consuming local resources (e.g., data-plans, computation and even energy resources), device-to-device (D2D) resource sharing is a promising approach towards realizing a…
Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor…
We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data…