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Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Concentration Of Measure And Isoperimetric Inequalities In Product Spaces
, 1995
"... . The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning ..."
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Cited by 383 (4 self)
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. The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning of the word "most" is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work "close" is defined in three main ways, each of them giving rise to related, but di#erent inequalities. The inequalities are all proved through a common scheme of proof. Remarkably, this simple approach not only yields qualitatively optimal results, but, in many cases, captures near optimal numerical constants. A large number of applications are given, in particular to Percolation, Geometric Probability, Probability in Banach Spaces, to demonstrate in concrete situations the extremely wide range of application of the abstract tools. AMS Classification numbers: Primary 60E15, 28A35, 60G99; Secondary 60G15, 68C15. Typeset by A M ST E X 1 2 M. TALAGRAND Table of Contents I.
Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 369 (11 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
THE DIAMETER OF RANDOM CAYLEY DIGRAPHS OF GIVEN DEGREE
"... Abstract. We consider random Cayley digraphs of order n with uniformly distributed generating set of size k. Specifically, we are interested in the asymptotics of the probability such a Cayley digraph has diameter two as n → ∞ and k = f(n). We find a sharp phase transition from 0 to 1 as the order ..."
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Cited by 2 (1 self)
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Abstract. We consider random Cayley digraphs of order n with uniformly distributed generating set of size k. Specifically, we are interested in the asymptotics of the probability such a Cayley digraph has diameter two as n → ∞ and k = f(n). We find a sharp phase transition from 0 to 1 as the order
Automorphism Groups and Isomorphisms of Cayley Digraphs of Abelian Groups*
"... Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2subgroup of G is cyclic, then Sand S U Sl are CIsubsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity element ..."
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Cited by 1 (0 self)
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Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2subgroup of G is cyclic, then Sand S U Sl are CIsubsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity
Random Cayley digraphs of diameter 2 and given degree
"... We consider random Cayley digraphs of order n with uniformly distributed generating sets of size k. Specifically, we are interested in the asymptotics of the probability that such a Cayley digraph has diameter two as n → ∞ and k = f(n), focusing on the functions f(n) = ⌊n δ ⌋ and f(n) = ⌊cn⌋. In ..."
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We consider random Cayley digraphs of order n with uniformly distributed generating sets of size k. Specifically, we are interested in the asymptotics of the probability that such a Cayley digraph has diameter two as n → ∞ and k = f(n), focusing on the functions f(n) = ⌊n δ ⌋ and f(n) = ⌊cn
CAYLEY DIGRAPHS OF FINITE ABELIAN GROUPS AND MONOMIAL IDEALS∗
"... Abstract. In the study of doubleloop computer networks, the diagrams known as Lshapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the ..."
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Cited by 1 (1 self)
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of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece
A Note on Isomorphisms of Cayley Digraphs of Abelian Groups *
"... Let Sand T be two minimal generating s~bsets of a finite abelian group G. We prove that if Cay(G, S) ~ Cay(G, T) then there exists an a E Aut(G) such that SOl = T. Let G be a finite group and S a subset of G not containing the identity element 1. The Cayley digraph X = Cay ( G, S) of G with respect ..."
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Let Sand T be two minimal generating s~bsets of a finite abelian group G. We prove that if Cay(G, S) ~ Cay(G, T) then there exists an a E Aut(G) such that SOl = T. Let G be a finite group and S a subset of G not containing the identity element 1. The Cayley digraph X = Cay ( G, S) of G
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