Related papers: Dynamic Planar Point Location in External Memory
Stencil computations on low dimensional grids are kernels of many scientific applications including finite difference methods used to solve partial differential equations. On typical modern computer architectures, such stencil computations…
Given two point sets $R$ and $B$ in the plane, with cardinalities $m$ and $n$, respectively, and each set stored in a separate R-tree, we present an algorithm to decide whether $R$ and $B$ are linearly separable. Our algorithm exploits the…
New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered…
We present efficient data structures for submatrix maximum queries in Monge matrices and Monge partial matrices. For $n\times n$ Monge matrices, we give a data structure that requires O(n) space and answers submatrix maximum queries in…
We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries…
We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in CGAL, the Computational Geometry Algorithms Library. We can now guarantee that…
In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given…
We consider the problem of laying out a tree with fixed parent/child structure in hierarchical memory. The goal is to minimize the expected number of block transfers performed during a search along a root-to-leaf path, subject to a given…
We consider a novel formulation of the dynamic pricing and demand learning problem, where the evolution of demand in response to posted prices is governed by a stochastic variant of the popular Bass model with parameters $\alpha, \beta$…
We study the problem of scheduling a general computational DAG on multiple processors in a 2-level memory hierarchy. This setting is a natural generalization of several prominent models in the literature, and it simultaneously captures…
In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann (STOC 2019) showed that exact distance queries on planar graphs could be answered in $n^{o(1)}$ time by a data structure occupying $n^{1+o(1)}$ space, i.e., up to…
Despite remarkable successes achieved by modern neural networks in a wide range of applications, these networks perform best in domain-specific stationary environments where they are trained only once on large-scale controlled data…
This paper addresses the problem of learning instantaneous occupancy levels of dynamic environments and predicting future occupancy levels. Due to the complexity of most real-world environments, such as urban streets or crowded areas, the…
The article discusses a generalization of model of economic growth with constant pace, which takes into account the effects of dynamic memory. Memory means that endogenous or exogenous variable at a given time depends not only on their…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
Given a finite set $X \subset \mathbb{R}^d$ and a binary linear classifier $c: \mathbb{R}^d \to \{0,1\}$, how many queries of the form $c(x)$ are required to learn the label of every point in $X$? Known as \textit{point location}, this…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
We describe algorithmic results for two crucial aspects of allocating resources on computational hardware devices with partial reconfigurability. By using methods from the field of computational geometry, we derive a method that allows…
The dynamic partial sorting problem asks for an algorithm that maintains lists of numbers under the link, cut and change value operations, and queries the sorted sequence of the $k$ least numbers in one of the lists. We first solve the…
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…