A Time-Space Trade-off for the Shortest Path Tree in a Simple Polygon

2018 ◽  
Vol 29 (03) ◽  
pp. 391-402
Author(s):  
Pardis Kavand ◽  
Ali Mohades
Keyword(s):  
Shortest Path ◽  
Simple Polygon ◽  
Shortest Path Tree ◽  
Trade Off ◽  
Time Space

A [Formula: see text]-workspace algorithm may use a workspace of [Formula: see text] words which can be read and written, in addition to their input, which is provided as a read-only array of [Formula: see text] items. We present a [Formula: see text]-workspace algorithm for constructing the shortest path tree of a simple polygon [Formula: see text] with [Formula: see text] vertices, with respect to a given point inside the polygon in [Formula: see text] time, where [Formula: see text] is the time for computing the visibility polygon of a given point inside a simple polygon with [Formula: see text] additional words of space.

OPTIMAL PARALLEL ALGORITHMS FOR TRIANGULATED SIMPLE POLYGONS

1995 ◽  
Vol 05 (01n02) ◽  
pp. 145-170 ◽  
Author(s):  
JOHN HERSHBERGER
Keyword(s):  
Convex Hull ◽  
Parallel Algorithms ◽  
Shortest Path ◽  
Simple Polygon ◽  
Implicit Representation ◽  
Shortest Path Tree ◽  
Simple Polygons ◽  
Pram Model ◽  
Crew Pram ◽  
Path Queries

We provide optimal parallel solutions to several shortest path and visibility problems set in triangulated simple polygons. Let P be a triangulated simple polygon with n vertices, preprocessed to support shortest path queries. We can find the shortest path tree from any point inside P in O(log n) time using O(n/log n) processors. In the game bounds, we can preprocess P for shooting queries (a query can be answered in O(log n) time by a uniprocessor). Given a set S of m points inside P, we can find an implicit representation of the relative convex hull of S in O(log(nm)) time with O(m) processors. If the relative convex hull has k edges, we can explicitly produce these edges in O(log(nm)) time with O(k/log(nm)) processors. All of these algorithms are deterministic and use the CREW PRAM model.

scholarly journals A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms

Algorithmica ◽  
2019 ◽  
Vol 81 (7) ◽  
pp. 2829-2856
Author(s):  
Eunjin Oh ◽  
Hee-Kap Ahn
Keyword(s):  
Simple Polygon ◽  
Trade Off ◽  
Time Space

scholarly journals A bi-level encoding scheme for the clustered shortest-path tree problem in multifactorial optimization

2021 ◽  
Vol 100 ◽  
pp. 104187 ◽  
Author(s):  
Huynh Thi Thanh Binh ◽  
Ta Bao Thang ◽  
Nguyen Duc Thai ◽  
Pham Dinh Thanh
Keyword(s):  
Shortest Path ◽  
Shortest Path Tree ◽  
Encoding Scheme

FINDING AN OPTIMAL BRIDGE BETWEEN TWO POLYGONS

2002 ◽  
Vol 12 (03) ◽  
pp. 249-261 ◽  
Author(s):  
XUEHOU TAN
Keyword(s):  
Hierarchical Structure ◽  
Shortest Path ◽  
Line Segment ◽  
Euclidean Distance ◽  
Geodesic Distance ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Search Trees ◽  
Bridge Problem ◽  
Path Queries

Let π(a,b) denote the shortest path between two points a, b inside a simple polygon P, which totally lies in P. The geodesic distance between a and b in P is defined as the length of π(a,b), denoted by gd(a,b), in contrast with the Euclidean distance between a and b in the plane, denoted by d(a,b). Given two disjoint polygons P and Q in the plane, the bridge problem asks for a line segment (optimal bridge) that connects a point p on the boundary of P and a point q on the boundary of Q such that the sum of three distances gd(p′,p), d(p,q) and gd(q,q′), with any p′ ∈ P and any q′ ∈ Q, is minimized. We present an O(n log 3 n) time algorithm for finding an optimal bridge between two simple polygons. This significantly improves upon the previous O(n2) time bound. Our result is obtained by making substantial use of a hierarchical structure that consists of segment trees, range trees and persistent search trees, and a structure that supports dynamic ray shooting and shortest path queries as well.

A Time-Space Trade-Off for Triangulations of Points in the Plane

2017 ◽  
pp. 3-12 ◽  
Author(s):  
Hee-Kap Ahn ◽  
Nicola Baraldo ◽  
Eunjin Oh ◽  
Francesco Silvestri
Keyword(s):  
Trade Off ◽  
Time Space

Shortest Path Tree Computation in Dynamic Graphs

2009 ◽  
Vol 58 (4) ◽  
pp. 541-557 ◽  
Author(s):  
E.P.F. Chan ◽  
Yaya Yang
Keyword(s):  
Shortest Path ◽  
Dynamic Graphs ◽  
Shortest Path Tree

Experimental Evaluation of Dynamic Shortest Path Tree Algorithms on Homogeneous Batches

2014 ◽  
pp. 283-294 ◽  
Author(s):  
Annalisa D’Andrea ◽  
Mattia D’Emidio ◽  
Daniele Frigioni ◽  
Stefano Leucci ◽  
Guido Proietti
Keyword(s):  
Shortest Path ◽  
Experimental Evaluation ◽  
Shortest Path Tree ◽  
Tree Algorithms

A New Algorithm for Euclidean Shortest Path of Visiting Segments in a Polygon

2014 ◽  
Vol 644-650 ◽  
pp. 1891-1894
Author(s):  
Li Juan Wang ◽  
An Sheng Deng ◽  
Bo Jiang ◽  
Qi Wei
Keyword(s):  
Test Data ◽  
Shortest Path ◽  
Time Complexity ◽  
Simple Polygon ◽  
Rubber Band ◽  
Crossing Over ◽  
Euclidean Shortest Path ◽  
Adjacent Segments ◽  
Improved Algorithm

Let s and t be two points on the boundary of a simple polygon, how to compute the Euclidean shortest path between s and t which visits a sequence of segments given in the simple polygon is the problem to be discussed, especially, the situation of the adjacent segments intersect is the focus of our study. In this paper, we first analyze the degeneration applying rubber-band algorithm to solve the problem. Then based on rubber-band algorithm, we present an improved algorithm which can solve the degeneration by the method of crossing over two segments to deal with intersection and in our algorithm the adjacent segments order can be changed when they intersect. Particularly, we have implemented the algorithm and have applied a large of test data to test it. The experiments demonstrate that our algorithm is correct and efficient, and it has the same time complexity as the rubber-band algorithm.

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