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Generalized loopback recovery in optical mesh networks
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2002
"... Current means of providing loopback recovery, which is widely used in SONET, rely on ring topologies, or on overlaying logical ring topologies upon physical meshes. Loopback is desirable to provide rapid preplanned recovery of link or node failures in a bandwidthefficient distributed manner. We i ..."
Abstract

Cited by 29 (4 self)
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Current means of providing loopback recovery, which is widely used in SONET, rely on ring topologies, or on overlaying logical ring topologies upon physical meshes. Loopback is desirable to provide rapid preplanned recovery of link or node failures in a bandwidthefficient distributed manner. We introduce generalized loopback, a novel scheme for performing loopback in optical mesh networks. We present an algorithm to perform recovery for link failure and one to perform generalized loopback recovery for node failure. We illustrate the operation of both algorithms, prove their validity, and present a network management protocol algorithm, which enables distributed operation for link or node failure. We present three different applications of generalized loopback. First, we present heuristic algorithms for selecting recovery graphs, which maintain short maximum and average lengths of recovery paths. Second, we present WDMbased loopback recovery for optical networks where wavelengths are used to back up other wavelengths. We compare, for WDMbased loopback, the operation of generalized loopback operation with known ringbased ways of providing loopback recovery over mesh networks. Finally, we introduce the use of generalized loopback to provide recovery in a way that allows dynamic choice of routes over preplanned directions.
The Complete Catalog of 3Regular, Diameter3 Planar Graphs
, 1996
"... The largest known 3regular planar graph with diameter 3 has 12 vertices. We consider the problem of determining whether there is a larger graph with these properties. We find all nonisomorphic 3regular, diameter3 planar graphs, thus solving the problem completely. There are none with more than 12 ..."
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Cited by 1 (1 self)
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The largest known 3regular planar graph with diameter 3 has 12 vertices. We consider the problem of determining whether there is a larger graph with these properties. We find all nonisomorphic 3regular, diameter3 planar graphs, thus solving the problem completely. There are none with more than 12 vertices. An Upper Bound A graph with maximum degree \Delta and diameter D is called a (\Delta; D)graph. It is easily seen ([9], p. 171) that the order of a (\Delta,D)graph is bounded above by the Moore bound, which is given by 1+ \Delta + \Delta (\Delta \Gamma 1) + \Delta \Delta \Delta + \Delta(\Delta \Gamma 1) D\Gamma1 = 8 ? ! ? : \Delta(\Delta \Gamma 1) D \Gamma 2 \Delta \Gamma 2 if \Delta 6= 2; 2D + 1 if \Delta = 2: Figure 1: The regular (3,3)graph on 20 vertices (it is unique up to isomorphism) . For D 2 and \Delta 3, this bound is attained only if D = 2 and \Delta = 3; 7, and (perhaps) 57 [3, 14, 23]. Now, except for the case of C 4 (the cycle on four vertices), the num...