Zobrazeno 1 - 10
of 936
pro vyhledávání: '"Sharir, Micha"'
Let $P$ be a set of $m$ points in ${\mathbb R}^2$, let $\Sigma$ be a set of $n$ semi-algebraic sets of constant complexity in ${\mathbb R}^2$, let $(S,+)$ be a semigroup, and let $w: P \rightarrow S$ be a weight function on the points of $P$. We desc
Externí odkaz:
http://arxiv.org/abs/2403.12276
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $d$-space into constant-complexity subcells. In this paper, we settle in the affirmative a few long-standing open problems i
Externí odkaz:
http://arxiv.org/abs/2311.01597
Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate inside $\math
Externí odkaz:
http://arxiv.org/abs/2310.20615
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between them is at mo
Externí odkaz:
http://arxiv.org/abs/2307.14663
Autor:
Cardinal, Jean, Sharir, Micha
In the classical linear degeneracy testing problem, we are given $n$ real numbers and a $k$-variate linear polynomial $F$, for some constant $k$, and have to determine whether there exist $k$ numbers $a_1,\ldots,a_k$ from the set such that $F(a_1,\ld
Externí odkaz:
http://arxiv.org/abs/2212.03030
Autor:
Ezra, Esther, Sharir, Micha
We develop data structures for intersection queries in four dimensions that involve segments, triangles and tetrahedra. Specifically, we study three main problems: (i) Preprocess a set of $n$ tetrahedra in $\reals^4$ into a data structure for answeri
Externí odkaz:
http://arxiv.org/abs/2208.06703
Autor:
Katz, Matthew J., Sharir, Micha
We present an algorithm for computing a bottleneck matching in a set of $n=2\ell$ points in the plane, which runs in $O(n^{\omega/2}\log n)$ deterministic time, where $\omega\approx 2.37$ is the exponent of matrix multiplication.
Externí odkaz:
http://arxiv.org/abs/2205.05887
Let $\mathcal{T}$ be a set of $n$ flat (planar) semi-algebraic regions in $\mathbb{R}^3$ of constant complexity (e.g., triangles, disks), which we call plates. We wish to preprocess $\mathcal{T}$ into a data structure so that for a query object $\gam
Externí odkaz:
http://arxiv.org/abs/2203.10241
Autor:
Katz, Matthew J., Sharir, Micha
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that they involve
Externí odkaz:
http://arxiv.org/abs/2111.02052
We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise disjoint segmen
Externí odkaz:
http://arxiv.org/abs/2109.07587