The dimension exchange method is a distributed load balancing method for point-to-point networks. We add a parameter, called the exchange parameter, to the method to control the splitting of load between a pair of directly connected processors, and call this parameterized version the generalized dimension exchange (GDE) method. The rationale for the introduction of this parameter is that splitting the workload into equal halves does not necessarily lead to an optimal result (in terms of the convergence rate) for certain structures. We carry out an analysis of this new method, emphasizing on its termination aspects and potential efficiency. Given a specific structure, one needs to determine a value to use for the exchange parameter that would lead to an optimal result. To this end, we first derive a sufficient and necessary condition for the termination of the method. We then show that equal splitting, proposed originally by others as a heuristic strategy, indeed yields optimal efficie...

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.

With nearest neighbor load balancing algorithms, a processor makes balancing decisions based on localized workload information and manages workload migrations within its neighborhood. This paper compares a couple of fairly well-known nearest neighbor algorithms, the dimension-exchange (DE, for short) and the diffusion (DF, for short) methods and their several variants---the average dimension-exchange (ADE), the optimally-tuned dimension-exchange (ODE), the local average diffusion (ADF) and the optimally-tuned diffusion (ODF). The measures of interest are their efficiency in driving any initial workload distribution to a uniform distribution and their ability in controlling the growth of the variance among the processors' workloads. The comparison is made with respect to both one-port and all-port communication architectures and in consideration of various implementation strategies including synchronous/asynchronous invocation policies and static/dynamic random workload behaviors. It t...

Graph structures have proved computationally cumbersome for pattern analy-sis. The reason for this is that before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this rep-resentation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian prop-erty matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low dimensional space using a number of alternative strategies including principal components analysis (PCA), multidimensional scaling (MDS) and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well defined graph clusters. Our experiments with the

Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The bounds are based on a projection technique developed for the quadratic assignment problem, and once more demonstrate the importance of the extreme eigenvalues of the Laplacian. They will be shown to be strict for certain classes of graphs and compare favourably to bounds already known in literature. Further improvement is gained by applying nonlinear optimization methods.

Graph grammars combine the relational aspect of graphs with the iterative and recursive aspects of string grammars, and thus represent an important next step in our ability to discover knowledge from data. In this paper we describe an approach to learning node replacement graph grammars. This approach is based on previous research in frequent isomorphic subgraphs discovery. We extend the search for frequent subgraphs by checking for overlap among the instances of the subgraphs in the input graph. If subgraphs overlap by one node we propose a node replacement grammar production. We also can infer a hierarchy of productions by compressing portions of a graph described by a production and then infer new productions on the compressed graph. We validate this approach in experiments where we generate graphs from known grammars and measure how well our system infers the original grammar from the generated graph. We also describe results on several real-world tasks from chemical mining to XML schema induction. We briefly discuss other grammar inference systems indicating that our study extends classes of learnable graph grammars.

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In an ordinary edge-coloring of a graph each color... This paper gives efficient sequential and parallel algorithms to find ordinary edge-colorings and f-colorings for various classes of graphs such as bipartite graphs, planar graphs, and graphs having fixed degeneracy, tree-width, genus, arboricity, unicyclic index or thickness.

. Vizing's theorem states that the chromatic index Ø 0 (G) of a graph G is either the maximum degree \Delta(G) or \Delta(G) + 1. A graph G is called overfull if jE(G)j ? \Delta(G)bjV (G)j=2c. A sufficient condition for Ø 0 (G) = \Delta(G) + 1 is that G contains an overfull subgraph H with \Delta(H ) = \Delta(G). Plantholt proved that this condition is necessary for graphs with a universal vertex. In this paper, we conjecture that, for indifference graphs, this is also true. As supporting evidence, we prove this conjecture for general graphs with three maximal cliques and with no universal vertex, and for indifference graphs with odd maximum degree. For the latter subclass, we prove that Ø 0 = \Delta. 1 Introduction An edge-colouring of a graph is an assignment of colours to its edges such that no adjacent edges have the same colour. The chromatic index of a graph is the minimum number of colours required to produce an edge-colouring for that graph. In this paper, we address...

We consider the problem of edge-coloring planar graphs. It is known that a planar graph G with maximum degree \Delta \geq 8 can be colored with \Delta colors. We present two algorithms which find such a coloring when \Delta \geq 9. The first one is a sequential O(n log n) time algorithm. The other one is a parallel EREW PRAM algorithm which works in time O(log³ n) and uses O(n) processors.