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- W2474262610 abstract "Routing is one of the basic tasks that any parallel or distributed system must be able to perform. A routing scheme is a mechanism that can deliver packets of information between any two nodes of the network. The goal is to find a routing scheme with low memory requirements (scheme compactness) and fast message passing mechanism (scheme efficiency) which forwards messages along shortest (optimal) or near optimal (low deviation) paths. Since it is not possible to design a compact routing scheme for an arbitrary network, we develop specific routing strategies for networks with certain topological properties. A network can be viewed as a graph, with the vertices representing processors and the edges representing direct connections between processors. We investigate some special graph classes from a graph-theoretical point of view and establish their properties useful for design of compact, efficient, and optimal routing schemes for communication networks that these graphs represent. Some graphs possess well-structured geometric models with properties of which allow construction of simple and efficient routing schemes for these graphs. Another approach for the routing scheme design is based of the notion of acyclic clustering. Namely, we show that, if the vertex set of a graph can be decomposed into a set of small diameter clusters in such a way that the clusters form a tree with special properties, then the graph admits an efficient and compact routing scheme of low deviation. The dissertation contains the following contributions: (1) For interval and circular-arc graphs we present the best known optimal and efficient routing schemes and the best known compact and efficient routing schemes of deviation 1. Additionally, we design a more compact routing scheme of deviation 2 for circular-arc graphs. As a byproduct we obtain the best possible routing schemes for proper interval and proper circular-arc graphs. (2) We present first routing schemes for permutation graphs, namely an efficient scheme of deviation 1 and an efficient and compact scheme of deviation 2. The latter scheme is extended to the class of trapezoid graphs. (3) For homogeneously orderable graphs we present first compact and efficient routing scheme of deviation 2." @default.
- W2474262610 created "2016-07-22" @default.
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- W2474262610 date "2005-01-01" @default.
- W2474262610 modified "2023-09-27" @default.
- W2474262610 title "Routing in special families of graphs" @default.
- W2474262610 hasPublicationYear "2005" @default.
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