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54
Protection Cycles in Mesh WDM Networks
 IEEE Journal on Selected Areas in Communications
, 2000
"... A fault recovery system that is fast and reliable is essential to today's networks, as it can be used to minimize the impact of the fault on the operation of the network and the services it provides. This paper proposes a methodology for performing automatic protection switching (APS) in optical net ..."
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Cited by 38 (0 self)
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A fault recovery system that is fast and reliable is essential to today's networks, as it can be used to minimize the impact of the fault on the operation of the network and the services it provides. This paper proposes a methodology for performing automatic protection switching (APS) in optical networks with arbitrary mesh topologies in order to protect the network from fiber link failures. All fiber links interconnecting the optical switches are assumed to be bidirectional. In the scenario considered, the layout of the protection fibers and the setup of the protection switches is implemented in nonreal time, during the setup of the network. When a fiber link fails, the connections that use that link are automatically restored and their signals are routed to their original destination using the protection fibers and protection switches. The protection process proposed is fast, distributed, and autonomous. It restores the network in real time, without relying on a central manager or a centralized database. It is also independent of the topology and the connection state of the network at the time of the failure.
Planarizing Graphs  A Survey and Annotated Bibliography
, 1999
"... Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results abo ..."
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Cited by 33 (0 self)
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Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results about vertex splitting, thickness, and crossing number are mostly of a structural nature. We also include a brief section on vertex deletion. We do not consider parallel algorithms, nor do we deal with online algorithms.
Graph Theory Methods For The Analysis Of Neural Connectivity Patterns
"... This paper summarizes a set of graph theory methods that are of special relevance to the computational analysis of neural connectivity patterns. Methods characterizing average measures of connectivity, similarity of connection patterns, connectedness and components, paths, walks and cycles, distance ..."
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Cited by 17 (1 self)
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This paper summarizes a set of graph theory methods that are of special relevance to the computational analysis of neural connectivity patterns. Methods characterizing average measures of connectivity, similarity of connection patterns, connectedness and components, paths, walks and cycles, distances, cluster indices, ranges and shortcuts, and node and edge cut sets are introduced and discussed in a neurobiological context. A set of Matlab functions implementing these methods is available for download at
On the Approximate Cyclic Reduction Preconditioner
 SIAM J. Sci. Comput
, 2000
"... We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using ma ..."
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Cited by 16 (3 self)
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We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using maximal independent sets for graph coarsening. A Schur complement approximation is constructed using a sequence of point Gaussian elimination steps. The resulting preconditioner has a transparant modular structure similar to the algoritmic structure of a multigrid Vcycle.
On The Distribution Of The Domination Number For Random Class Cover Catch Digraphs
, 2001
"... In this article we initiate the class cover catch digraphs, a special caseoef==wIfMx: digraphs moraphsf by applicatiox in machine learning and statistical patternreconfxjx=I Our main result is the exact distributio o the doA=I=fM numberfo a datadrivenmota o rando interval catch digraphs. c 20 ..."
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Cited by 13 (7 self)
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In this article we initiate the class cover catch digraphs, a special caseoef==wIfMx: digraphs moraphsf by applicatiox in machine learning and statistical patternreconfxjx=I Our main result is the exact distributio o the doA=I=fM numberfo a datadrivenmota o rando interval catch digraphs. c 2001 Elsevier Science B.V. All rights reserved Keywords:Rando graph;Intersectio digraph;Doaph;fxx number;Distributio 1. CL52 cover catch digraphs }, Y= 1 ;:::;Y m betwo classeso valuedrando variables with johf F X;Y . Let d(; ):R [0; #) be any distance functiof The class cover problemfo a distinguished target class (say, X;no that theprow[x is asymmetric in target class) isto #nd acojx[fMw= oojx ballsB (c i ;r i ):={x: d(x; c i ) r i such that (i) X i and (ii) Y . Aco:A[fMwA oo:A[ satisfying (i) and (ii) is termed a class cover.
Algorithms and Obstructions for LinearWidth and Related Search Parameters
 Discrete Applied Mathematics
, 1997
"... The linearwidth of a graph G is defined to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e 1 ; : : : ; e r ) in such a way that for every i = 1; : : : ; r \Gamma 1, there are at most k vertices incident to edges that belong both to fe 1 ; : : : ; e i g an ..."
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Cited by 11 (5 self)
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The linearwidth of a graph G is defined to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e 1 ; : : : ; e r ) in such a way that for every i = 1; : : : ; r \Gamma 1, there are at most k vertices incident to edges that belong both to fe 1 ; : : : ; e i g and to fe i+1 ; : : : ; e r g. In this paper, we give a set of 57 graphs and prove that it is the set of the minimal forbidden minors for the class of graphs with linearwidth at most two. Our proof also gives a linear time algorithm that either reports that a given graph has linearwidth more than two or outputs an edge ordering of minimum linearwidth. We further prove a structural connection between linearwidth and the mixed search number which enables us to determine, for any k 1, the set acyclic forbidden minors for the class of graphs with linearwidth k. Moreover, due to this connection, our algorithm can be transfered to two linear time algorithms that check whether a graph has mixe...
A mobility and traffic generation framework for modeling and simulating ad hoc communication networks
, 2004
"... ..."
On the Power of Deterministic Transitive Closures
 INFORMATION AND COMPUTATION
, 1995
"... We show that transitive closure logic (FO + TC) is strictly more powerful than deterministic transitive closure logic (FO + DTC) on finite (unordered) structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every DTCquery is bounded and the ..."
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Cited by 10 (1 self)
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We show that transitive closure logic (FO + TC) is strictly more powerful than deterministic transitive closure logic (FO + DTC) on finite (unordered) structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every DTCquery is bounded and therefore first order expressible. On the other hand there are simple (FO + pos TC) queries on these classes that cannot be defined by first order formulae.
The Crossing Number of a Graph on a Compact 2Manifold
, 1996
"... INTRODUCTION We assume that the reader is familiar with the basic concepts of graph theory as in [CL86] and the basic concepts of topological graph theory as in [WB78]. By the famous theorem of Brahana [Br23], any compact article no. 0069 105 00018708#96 #18.00 Copyright # 1996 by Academic Press ..."
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Cited by 8 (4 self)
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INTRODUCTION We assume that the reader is familiar with the basic concepts of graph theory as in [CL86] and the basic concepts of topological graph theory as in [WB78]. By the famous theorem of Brahana [Br23], any compact article no. 0069 105 00018708#96 #18.00 Copyright # 1996 by Academic Press, Inc. All rights of reproduction in any form reserved. * Research of the third author was supported by the A. v. HumboldtStiftung while he was at the Institut fu# r diskrete Mathematik, Bonn; and by the U. S. Office of Naval Research under the contract N001491J1385. File: 607J 155202 By:CV . Date:21:11:96 Time:08:36 LOP8M. V8.0. Page 01:01 Codes: 3060 Signs: 2268 Length: 45 pic 0 pts, 190 mm 2manifold is topologically equivalent either to a sphere with g#0 handles, S g (orientable surface with genus g), or to a sphere