On the Cost of Participating in a Peer-to-Peer Network

In this paper, we model the cost incurred by each peer participating in a peer-to-peer network. Such a cost model allows to gauge potential disincentives for peers to collaborate, and provides a measure of the ``total cost'' of a network, which is a possible benchmark to distinguish between proposals. We characterize the cost imposed on a node as a function of the experienced load and the node connectivity, and show how our model applies to a few proposed routing geometries for distributed hash tables (DHTs). We further outline a number of open questions this research has raised.Comment: 17 pages, 4 figures. Short version to be published in the Proceedings of the Third International Workshop on Peer-to-Peer Systems (IPTPS'04). San Diego, CA. February 200

How Graph Theory can help Communications Engineering

International audienceWe give an overview of different aspects of graph theory which can be applied in communication engineering, not trying to present immediate results to be applied neither a complete survey of results, but to give a flavor of how graph theory can help this field. We deal in this paper with network topologies, resource competition, state transition diagrams and specific models for optical networks

Topologies for Optical Interconnection Networks Based on the Optical Transpose Interconnection System

International audienceMany results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graph-theoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and de Bruijn digraphs

An application of a genetic algorithm for throughput optimization in non-broadcast WDM optical networks with regular topologies

We apply a genetic algorithm from Podnar and Skorin-Kapov [5] to a virtual topology design of a Wide-Area WDM Optical Network with regular topologies. Based on a given physical topology a virtual topology consisting of optical lightpaths is constructed. The objective is to minimize the maximal throughput, which implies balancing link loads and accommodating on-growing traffic requirements in a timely fashion. The genetic algorithm is applied to benchmark instances of regular topologies

Optimal transmission schedules for lightwave networks embedded with de Bruijn graphs

AbstractWe consider the problem of embedding a virtual de Bruijn topology, both directed and undirected, in a physical optical passive star time and wavelength division multiplexed (TWDM) network and constructing a schedule to transmit packets along all edges of the virtual topology in the shortest possible time. We develop general graph theoretic results and algorithms and using these build optimal embeddings and optimal transmission schedules, assuming certain conditions on the network parameters. We prove our transmission schedules are optimal over all possible embeddings.As a general framework we use a model of the passive star network with fixed tuned receivers and tunable transmitters. Our transmission schedules are optimal regardless of the tuning time. Our results are also applicable to models with one or more fixed tuned transmitters per node. We give results that minimize the number of tunings needed. For the directed de Bruijn topology a single fixed tuning of the transmitter suffices. For the undirected de Bruijn topology two tunings per cycle (or two fixed tuned transmitters per node) suffice and we prove this is the minimum possible

Logical Embeddings for Minimum Congestion Routing in Lightwave Networks

The problem considered in this paper is motivated by the independence between logical and physical topology in Wavelength Division Multiplexing WDM based local and metropolitan lightwave networks. This paper suggests logical embeddings of digraphs into multihop lightwave networks to maximize the throughput under nonuniform traffic conditions. Defining congestion as the maximum flow carried on any link, two perturbation heuristics are presented to find a good logical embedding on which the routing problem is solved with minimum congestion. A constructive proof for a lower bound of the problem is given, and obtaining an optimal solution for integral routing is shown to be NP-Complete. The performance of the heuristics is empirically analyzed on various traffic models. Simulation results show that our heuristics perform on the average from a computed lower bound Since this lower bound is not quite tight we suspect that the actual performance is better In addition we show that 5%-20% performance improvements can be obtained over the previous work