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Approximation Algorithms for Survivable Optical Networks (Extended Abstract)
 In The 14th international Symposium on Distributed Computing (DISC
, 2000
"... ) T. Eilam S. Moran S. Zaks Department of Computer Science The Technion Haifa 32000, Israel email: feilam,moran,zaksg@cs.technion.ac.il We are motivated by the developments in alloptical networks  a new technology that supports high bandwidth demands. These networks provide a set of lightpa ..."
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) T. Eilam S. Moran S. Zaks Department of Computer Science The Technion Haifa 32000, Israel email: feilam,moran,zaksg@cs.technion.ac.il We are motivated by the developments in alloptical networks  a new technology that supports high bandwidth demands. These networks provide a set of lightpaths which can be seen as highbandwidth pipes on which communication is performed. Since the capacity enabled by this technology substantially exceeds the one provided by conventional networks, its ability to recover from failures within the optical layer is important. In this paper we study the design of a survivable optical layer. We assume that an initial set of lightpaths (designed according to the expected communication pattern) is given, and we are targeted at augmenting this initial set with additional lightpaths such that the result will guarantee survivability. For this purpose, we define and motivate a ring partition survivability condition that the solution must satisfy. Generally...
Scenic Graphs II: NonTraceable Graphs
"... A path of a graph is maximal if it is not a proper subpath of any other path of the graph. A graph is scenic if every maximal path of the graph is a maximum length path. In [4] we give a new proof of C. Thomassen's result characterizing all scenic graphs with Hamiltonian path. Using similar met ..."
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A path of a graph is maximal if it is not a proper subpath of any other path of the graph. A graph is scenic if every maximal path of the graph is a maximum length path. In [4] we give a new proof of C. Thomassen's result characterizing all scenic graphs with Hamiltonian path. Using similar methods here we determine all scenic graphs with no Hamiltonian path. 1
Lightpath Arrangement in Survivable Rings to Minimize the Switching Cost
"... Abstract—This paper studies the design of lowcost survivable wavelengthdivisionmultiplexing (WDM) networks. To achieve survivability, lightpaths are arranged as a set of rings. Arrangement in rings is also necessary to support SONET/SDH protection schemes such as 4FBLSR above the optical layer. T ..."
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Abstract—This paper studies the design of lowcost survivable wavelengthdivisionmultiplexing (WDM) networks. To achieve survivability, lightpaths are arranged as a set of rings. Arrangement in rings is also necessary to support SONET/SDH protection schemes such as 4FBLSR above the optical layer. This is expected to be the most common architecture in regional (metro) networks [9]. We assume that we are given a set of lightpaths in an arbitrary network topology and aim at finding a partition of the lightpaths to rings adding a minimum number of lightpaths to the original set. The cost measure that we consider (number of lightpaths) reflects the switching cost of the entire network. In the case of a SONET/SDH higher layer, the number of lightpaths is equal to the number of adddrop multiplexers (ADMs) (since two subsequent lightpaths in a ring can share an ADM at the common node). We prove some negative results on the tractability and approximability of the problem and provide an approximation algorithm with a worst case approximation ratio of 8/5. We study some special cases in which the performance of the algorithm is improved. A similar problem was introduced, motivated, and studied in [9] and recently in [13] (where it was termed minimum ADM problem). However, these two works focused on a ring topology while we generalize the problem to an arbitrary network topology. Index Terms—Optical network design, SONET add/drop multiplexers (ADMs), SONET rings, wavelengthdivision multiplexing (WDM).
Abstract Note Randomly planar graphs
, 1997
"... A graph G is randomly planar if every planar embedding of every connected subgraph of G can be extended to a planar embedding of G. We classify these graphs. 1. ..."
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A graph G is randomly planar if every planar embedding of every connected subgraph of G can be extended to a planar embedding of G. We classify these graphs. 1.
On the EXISTENCE of SPECIAL DEPTH FIRST SEARCH TREES
"... The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depthfirst spanning tree (DFS tree). In this paper, we give a complete characterization of all the graphs in w ..."
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The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depthfirst spanning tree (DFS tree). In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total DFSGraphs. We prove that Total DFSGraphs are closed under minors. It follows by the work of Robertson and Seymour on graph minors, that there is a finite set of forbidden minors of these graphs and that there is a polynomial algorithm for their recognition. We also provide explicit characterizations of these graphs in terms of forbidden minors and forbidden topological minors. The complete characterization implies explicit linear algorithm for their recognition. In some problems the degree of some vertices in the DFS tree obtained in a certain run are crucial and therefore we also consider the following problem: Let G...