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The Diameter of Randomly Perturbed Digraphs and Some Applications
"... The central observation of this paper is that if n random edges are added to any nnode connected graph or digraph then the resulting graph has diameter O(log n). We apply this to smoothed analysis of algorithms and property testing. ..."
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Cited by 17 (3 self)
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The central observation of this paper is that if n random edges are added to any nnode connected graph or digraph then the resulting graph has diameter O(log n). We apply this to smoothed analysis of algorithms and property testing.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
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
Algebraic Decision Diagrams and their Applications
, 1993
"... In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and ..."
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Cited by 316 (17 self)
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and results in applications like matrix multiplication and shortest path algorithms. Furthermore, we outline possible applications of ADD's to logic synthesis, formal verification, and testing of digital systems.
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
Random Cayley Digraphs and the Discrete Logarithm
 ANTSV), Lecture Notes in Computer Science
, 2002
"... Abstract. We formally show that there is an algorithm for dlog over all abelian groups that runs in expected optimal time (up to logarithmic factors) and uses only a small amount of space. To our knowledge, this is the first such analysis. Our algorithm is a modification of the classic Pollard rho, ..."
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Cited by 4 (1 self)
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, introducing explicit randomization of the parameters for the updating steps of the algorithm, and is analyzed using random walks with limited independence over abelian groups (a study which is of its own interest). Our analysis shows that finding cycles in such large graphs over groups that can be efficiently
Results 1  10
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2,359