Information Bounds Are Weak in the Shortest Distance Problem

1980 ◽  
Vol 27 (3) ◽  
pp. 428-444 ◽  
Author(s):  
Ronald L. Graham ◽  
Andrew C. Yao ◽  
F. Frances Yao
Keyword(s):  
Shortest Distance ◽  
Distance Problem

ON THE COMPUTATION OF THE RELATIVE ENTROPY OF PROBABILISTIC AUTOMATA

2008 ◽  
Vol 19 (01) ◽  
pp. 219-242 ◽  
Author(s):  
CORINNA CORTES ◽  
MEHRYAR MOHRI ◽  
ASHISH RASTOGI ◽  
MICHAEL RILEY
Keyword(s):  
Machine Learning ◽  
Relative Entropy ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Probabilistic Automaton ◽  
Probabilistic Automata ◽  
Gaussian Kernels ◽  
Shortest Distance ◽  
Distance Problem ◽  
Number Of Publications

We present an exhaustive analysis of the problem of computing the relative entropy of two probabilistic automata. We show that the problem of computing the relative entropy of unambiguous probabilistic automata can be formulated as a shortest-distance problem over an appropriate semiring, give efficient exact and approximate algorithms for its computation in that case, and report the results of experiments demonstrating the practicality of our algorithms for very large weighted automata. We also prove that the computation of the relative entropy of arbitrary probabilistic automata is PSPACE-complete. The relative entropy is used in a variety of machine learning algorithms and applications to measure the discrepancy of two distributions. We examine the use of the symmetrized relative entropy in machine learning algorithms and show that, contrarily to what is suggested by a number of publications in that domain, the symmetrized relative entropy is neither positive definite symmetric nor negative definite symmetric, which limits its use and application in kernel methods. In particular, the convergence of training for learning algorithms is not guaranteed when the symmetrized relative entropy is used directly as a kernel, or as the operand of an exponential as in the case of Gaussian Kernels. Finally, we show that our algorithm for the computation of the entropy of an unambiguous probabilistic automaton can be generalized to the computation of the norm of an unambiguous probabilistic automaton by using a monoid morphism. In particular, this yields efficient algorithms for the computation of the Lp-norm of a probabilistic automaton.

scholarly journals A New Algorithm for Distributed Control Problem with Shortest-Distance Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yu Zhou ◽  
Wenfeng Zheng ◽  
Zhixi Shen
Keyword(s):  
Distributed Control ◽  
Multiagent Systems ◽  
Local Information ◽  
Common Point ◽  
Consensus Algorithm ◽  
Time Dynamics ◽  
Shortest Distance ◽  
Distributed Control Problem ◽  
Distance Problem ◽  
Theoretical Results

This paper investigates the distributed shortest-distance problem of multiagent systems where agents satisfy the same continuous-time dynamics. The objective of multiagent systems is to find a common point for all agents to minimize the sum of the distances from each agent to its corresponding convex region. A distributed consensus algorithm is proposed based on local information. A sufficient condition also is given to guarantee the consensus. The simulation example shows that the distributed shortest-distance consensus algorithm is effective for our theoretical results.

O(1) QUERY TIME ALGORITHM FOR ALL PAIRS SHORTEST DISTANCES ON INTERVAL GRAPHS

1999 ◽  
Vol 10 (04) ◽  
pp. 465-472 ◽  
Author(s):  
ALAN P. SPRAGUE ◽  
TADAO TAKAOKA
Keyword(s):  
Time Algorithm ◽  
Interval Graph ◽  
Query Time ◽  
Circular Arc ◽  
Interval Model ◽  
Erew Pram ◽  
Pram Model ◽  
Shortest Distance ◽  
Distance Problem ◽  
Circular Arc Graphs

We present an algorithm for the All Pairs Shortest Distance problem on an interval graph on n vertices: after O(n) preprocessing time, the algorithm can deliver a response to a distance query in O(1) time. The method used here is simpler than the method of Chen et al. [4], which has the same preprocessing and query time. It is assumed that an interval model for the graph is given, and ends of intervals are already sorted by coordinate. The preprocessing algorithm can be executed in the EREW PRAM model in O( log n) time, using n/ log n processors. These algorithms (sequential and parallel) may be extended to circular arc graphs, with the same time and processor bounds.

Path Planning of Mobile Robot Using Improved Artificial Bee Colony Algorithm

2020 ◽  
Vol 38 (9A) ◽  
pp. 1384-1395
Author(s):  
Rakaa T. Kamil ◽  
Mohamed J. Mohamed ◽  
Bashra K. Oleiwi
Keyword(s):  
Mobile Robot ◽  
Comparative Research ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Dynamic Control ◽  
Computational Time ◽  
Bee Colony ◽  
Shortest Distance ◽  
Minimum Number ◽  
Cubic Polynomial

A modified version of the artificial Bee Colony Algorithm (ABC) was suggested namely Adaptive Dimension Limit- Artificial Bee Colony Algorithm (ADL-ABC). To determine the optimum global path for mobile robot that satisfies the chosen criteria for shortest distance and collision–free with circular shaped static obstacles on robot environment. The cubic polynomial connects the start point to the end point through three via points used, so the generated paths are smooth and achievable by the robot. Two case studies (or scenarios) are presented in this task and comparative research (or study) is adopted between two algorithm’s results in order to evaluate the performance of the suggested algorithm. The results of the simulation showed that modified parameter (dynamic control limit) is avoiding static number of limit which excludes unnecessary Iteration, so it can find solution with minimum number of iterations and less computational time. From tables of result if there is an equal distance along the path such as in case A (14.490, 14.459) unit, there will be a reduction in time approximately to halve at percentage 5%.

scholarly journals Initial Clinical Experience With a New Conformable Abdominal Aortic Endograft: Aortic Neck Coverage and Curvature Analysis in Challenging Aortic Necks

2021 ◽  
pp. 152660282199672
Author(s):  
Alice Finotello ◽  
Richte Schuurmann ◽  
Sara Di Gregorio ◽  
Gian Antonio Boschetti ◽  
Nabil Chakfé ◽  
...  
Keyword(s):  
Aortic Wall ◽  
Surface Coverage ◽  
Infrarenal Aorta ◽  
Technical Success ◽  
Curvature Analysis ◽  
Average Curvature ◽  
Aortic Neck ◽  
Abdominal Aortic ◽  
Shortest Distance ◽  
New Generation

Objectives: Aim of this work was to investigate precision of deployment and conformability of a new generation GORE EXCLUDER Conformable Endoprosthesis with active control system (CEXC Device, W.L. Gore and Associates, Flagstaff, AZ, USA) by analyzing aortic neck coverage and curvature. Methods: All consecutive elective patients affected by abdominal aortic aneurysm or aortoiliac aneurysm treated at our institution between November 2018 and June 2019 with the new CEXC Device were enrolled. Validated software was adopted to determine the available apposition surface area into the aortic neck, apposition of the endograft to the aortic wall, shortest apposition length (SAL), shortest distance between the endograft fabric and the lowest renal arteries (SFD) and between the endograft fabric and the contralateral renal artery (CFD). Pointwise centerline curvature was also computed. Results: Twelve patients (10 men, median age 78 years (71.75, 81.0)) with available pre- and postoperative computed tomography angiography (CTA) were included. Technical success was obtained in all the cases. Preoperative median length of the proximal aortic neck was 16.1 mm (10.7, 21.7) and suprarenal (α) and infrarenal (β) neck angulation were, respectively, 28.9° (15.7°, 47.5°) and 75.0° (66.9°, 81.4°). Postoperative median apposition surface coverage was 79% (69.25%, 90.75%) of the available apposition surface. SFD and CFD were 1.5 mm (0.75, 5.25) and 7 mm (4.5, 21.5), respectively. Average curvature over the infrarenal aorta decreased from 25 m−1 (21.75, 29.0) to 22.5 m−1 (18.75, 24.5) postoperatively (p=0.02). Maximum curvature did not decrease significantly from 64.5 m−1 (54.25, 92.0) to 62 m−1 (41.75, 71.5) (p=0.1). Conclusions: Our early experience showed that deployment of the CEXC Device is safe and effective for patients with challenging proximal aortic necks. Absence of significant changes between pre- and postoperative proximal aortic neck angulations and curvature confirms the high conformability of this endograft.

scholarly journals An improved FPT algorithm for the flip distance problem

2021 ◽  
pp. 104708
Author(s):  
Qilong Feng ◽  
Shaohua Li ◽  
Xiangzhong Meng ◽  
Jianxin Wang
Keyword(s):  
Fpt Algorithm ◽  
Distance Problem ◽  
Flip Distance
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