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.

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.

Fast and Effective Copy-Move Detection of Digital Audio Based on Auto Segment

2019 ◽  
Vol 11 (2) ◽  
pp. 47-62 ◽  
Author(s):  
Xinchao Huang ◽  
Zihan Liu ◽  
Wei Lu ◽  
Hongmei Liu ◽  
Shijun Xiang
Keyword(s):  
Time Complexity ◽  
State Of The Art ◽  
Digital Audio ◽  
Activity Detection ◽  
Research Focus ◽  
Audio Forensics ◽  
Significant Research ◽  
Audio Data ◽  
Adjacent Segments ◽  
Voice Activity

Detecting digital audio forgeries is a significant research focus in the field of audio forensics. In this article, the authors focus on a special form of digital audio forgery—copy-move—and propose a fast and effective method to detect doctored audios. First, the article segments the input audio data into syllables by voice activity detection and syllable detection. Second, the authors select the points in the frequency domain as feature by applying discrete Fourier transform (DFT) to each audio segment. Furthermore, this article sorts every segment according to the features and gets a sorted list of audio segments. In the end, the article merely compares one segment with some adjacent segments in the sorted list so that the time complexity is decreased. After comparisons with other state of the art methods, the results show that the proposed method can identify the authentication of the input audio and locate the forged position fast and effectively.

Planning the Shortest Path in Cluttered Environments: A Review and a Planar Convex Hull-Based Approach

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Time Complexity ◽  
Optimal Path ◽  
Optimal Solution ◽  
Free Graph ◽  
Worst Case ◽  
Cluttered Environments ◽  
Planar Convex ◽  
Polyhedral Obstacles

Abstract Routing or path-planning is the problem of finding a collision-free and preferably shortest path in an environment usually scattered with polygonal or polyhedral obstacles. The geometric algorithms oftentimes tackle the problem by modeling the environment as a collision-free graph. Search algorithms such as Dijkstra’s can then be applied to find an optimal path on the created graph. Previously developed methods to construct the collision-free graph, without loss of generality, explore the entire workspace of the problem. For the single-source single-destination planning problems, this results in generating some unnecessary information that has little value and could increase the time complexity of the algorithm. In this paper, first a comprehensive review of the previous studies on the path-planning subject is presented. Next, an approach to address the planar problem based on the notion of convex hulls is introduced and its efficiency is tested on sample planar problems. The proposed algorithm focuses only on a portion of the workspace interacting with the straight line connecting the start and goal points. Hence, we are able to reduce the size of the roadmap while generating the exact globally optimal solution. Considering the worst case that all the obstacles in a planar workspace are intersecting, the algorithm yields a time complexity of O(n log(n/f)), with n being the total number of vertices and f being the number of obstacles. The computational complexity of the algorithm outperforms the previous attempts in reducing the size of the graph yet generates the exact solution.

OPTIMUM CONGESTED ROUTING STRATEGY ON TWISTED CUBES

2000 ◽  
Vol 01 (02) ◽  
pp. 115-134 ◽  
Author(s):  
TSENG-KUEI LI ◽  
JIMMY J. M. TAN ◽  
LIH-HSING HSU ◽  
TING-YI SUNG
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Optimum Time ◽  
Shortest Path Routing ◽  
Routing Strategy ◽  
Bisection Width ◽  
Twisted Cube ◽  
Twisted Cubes

Given a shortest path routing algorithm of an interconnection network, the edge congestion is one of the important factors to evaluate the performance of this algorithm. In this paper, we consider the twisted cube, a variation of the hypercube with some better properties, and review the existing shortest path routing algorithm8. We find that its edge congestion under the routing algorithm is high. Then, we propose a new shortest path routing algorithm and show that our algorithm has optimum time complexity O(n) and optimum edge congestion 2n. Moreover, we calculate the bisection width of the twisted cube of dimension n.

LOGARITHMIC-TIME LINK PATH QUERIES IN A SIMPLE POLYGON

1995 ◽  
Vol 05 (04) ◽  
pp. 369-395 ◽  
Author(s):  
ESTHER M. ARKIN ◽  
JOSEPH S.B. MITCHELL ◽  
SUBHASH SURI
Keyword(s):  
Data Structure ◽  
Shortest Path ◽  
Simple Polygon ◽  
Additive Constant ◽  
Time And Space ◽  
Link Distance ◽  
Path Distance ◽  
Path Queries ◽  
Shortest Path Distance ◽  
Small Additive

We develop a data structure for answering link distance queries between two arbitrary points in a simple polygon. The data structure requires O(n3) time and space for its construction and answers link distance queries in O(log n) time, after which a minimum-link path can be reported in time proportional to the number of links. Here, n denotes the number of vertices of the polygon. Our result extends to link distance queries between pairs of segments or polygons. We also propose a simpler data structure for computing a link distance approximately, where the error is bounded by a small additive constant. Finally, we also present a scheme for approximating the link and the shortest path distance simultaneously.

Precision-Sensitive Euclidean Shortest Path in 3-Space

2000 ◽  
Vol 29 (5) ◽  
pp. 1577-1595 ◽  
Author(s):  
Jürgen Sellen ◽  
Joonsoo Choi ◽  
Chee-Keng Yap
Keyword(s):  
Shortest Path ◽  
Euclidean Shortest Path

Improved Algorithm of Global Model-Checking for Propositional μ-Calculus

2012 ◽  
Vol 263-266 ◽  
pp. 2314-2319
Author(s):  
Hua Jiang ◽  
Jian Qing Xi
Keyword(s):  
Model Checking ◽  
Time Complexity ◽  
Transition System ◽  
Global Model ◽  
Space Complexity ◽  
Partial Ordering ◽  
Improved Algorithm

Based on the research of the author when he was a Ph.D. student, he deeply studied the proposition of μ-Calculus, and used solving the partial ordering relation in formula μ-Calculus to solve formula μ-Calculus quickly. This paper improves and perfects the algorithm in reference [11]. The time complexity of the algorithm in this paper is O((2n+1)^(d/2+1)), its space complexity is O(dn), where n is the number of states in the transition system and d is the nesting depth of fixpoint operators in the formula of proposition μ-Calculus.

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