Geometric Data Structures

Goodrich, Michael T.; Ramaiyer, Kumar

doi:10.1016/b978-044482537-7/50011-5

Cited by 4 publications

(4 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5 for an illustration. We store the relevant arrangement using standard data structures for planar arrangements [19], so that we can follow the edges of each face in clockwise or counter-clockwise direction efficiently (i.e., we can go from one edge to the next in constant time) and move from an edge of a face to the instance of the same edge in the adjacent face in constant time. This representation also allows us to to trace the lower envelope of Ψ in time O(k).…”

Section: Geometric Representation and Preprocessingmentioning

confidence: 99%

On the fast delivery problem with one or two packages

Carvalho

Erlebach

Papadopoulos

2021

Journal of Computer and System Sciences

View full text Add to dashboard Cite

Section: Geometric Representation and Preprocessingmentioning

confidence: 99%

On the fast delivery problem with one or two packages

Carvalho

Erlebach

Papadopoulos

2021

Journal of Computer and System Sciences

View full text Add to dashboard Cite

“…5 for an illustration. We store the relevant arrangement using standard data structures for planar arrangements [13], so that we can follow the edges of each face in clockwise or counterclockwise direction efficiently (i.e., we can go from one edge to the next in constant time) and move from an edge of a face to the instance of the same edge in the adjacent face in constant time. This representation also allows us to to trace the lower envelope of Ψ in time O(k).…”

Section: Main Algorithmmentioning

confidence: 99%

An Efficient Algorithm for the Fast Delivery Problem

Carvalho

Erlebach

Papadopoulos

2019

Fundamentals of Computation Theory

View full text Add to dashboard Cite

We study a problem where k autonomous mobile agents are initially located on distinct nodes of a weighted graph (with n nodes and m edges). Each autonomous mobile agent has a predefined velocity and is only allowed to move along the edges of the graph. We are interested in delivering a package, initially positioned in a source node s, to a destination node y. The delivery is achieved by the collective effort of the autonomous mobile agents, which can carry and exchange the package among them. The objective is to compute a delivery schedule that minimizes the delivery time of the package. In this paper, we propose an O(kn log n + km) time algorithm for this problem. This improves the previous state-of-the-art O(k 2 m + kn 2 + APSP) time algorithm for this problem, where APSP stands for the running-time of an algorithm for the All-Pairs Shortest Paths problem.

show abstract

“…Geometric search problems have a long and rich history [2,26,36]. In these problems, we are typically given a collection S of n geometric objects in R d and asked to store them in a data structure so that we can efficiently answer queries about these objects.…”

Section: Introductionmentioning

confidence: 99%

Odds-On Trees

Bose,

Devroye,

Douieb

et al. 2010

Preprint

View full text Add to dashboard Cite

Let P : R d → A be a query problem over R d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q ∈ R d . Let D be a probability measure over R d representing a distribution of queries. We describe a data structure T = T P,D , called the odds-on tree, of size O(n ) that can be used as a filter that quickly computes P(q) for some query values in R d and relies on S for the remaining queries. With an odds-on tree, the expected query time for a point drawn according to D is O(H * + 1), where H * is a lower-bound on the expected cost of any linear decision tree that solves P.Odds-on trees have a number of applications, including distribution-sensitive data structures for point location in 2-d, point-in-polytope testing in d dimensions, ray shooting in simple polygons, ray shooting in polytopes, nearest-neighbour queries in R d , pointlocation in arrangements of hyperplanes in R d , and many other geometric searching problems that can be solved in the linear-decision tree model. A standard lifting technique extends these results to algebraic decision trees of constant degree. A slightly different version of odds-on trees yields similar results for orthogonal searching problems that can be solved in the comparison tree model.

show abstract

Geometric Data Structures

Cited by 4 publications

References 56 publications

On the fast delivery problem with one or two packages

On the fast delivery problem with one or two packages

An Efficient Algorithm for the Fast Delivery Problem

Odds-On Trees

Contact Info

Product

Resources

About