Joseph G. Peters

Deterministic small-world communication networks

Abstract Many real life networks, including the World Wide Web, electric power grids, and social networks, are small-world networks . The two distinguishing characteristics of small-world networks are strong local clustering (nodes have many mutual neighbors), and small average distance between two nodes. Small-world networks are promising candidates for communication networks since typical data-flow patterns in communication networks show a large amount of clustering with a small number of “long-distance” communications that need to be completed quickly. Most previous research on small-world networks has used simulations, probabilistic techniques, and random replacements of edges to study the limiting behaviour of these networks. In this paper, we initiate the study of small-world networks as communication networks using graph-theoretic methods to obtain exact results. We construct networks with strong local clustering and small diameter (instead of average distance). Our networks have the additional property that they are regular .

Circuit-switched broadcasting in torus networks

In this paper we present three broadcast algorithms and lower bounds on the three main components of the broadcast time for 2-dimensional torus networks (wrap-around meshes) that use synchronous circuit-switched routing. The first algorithm is based on a recursive tiling of a torus and is optimal in terms of both phases and intermediate switch settings when the start-up time to initiate message transmissions is the dominant cost. It is the first broadcast algorithm to match the lower bound of log/sub 5/ N on number of phases (where N is the number of nodes). The second and third algorithms are hybrids which combine circuit-switching with the pipelining and arc-disjoint spanning trees techniques that are commonly used to speed up store-and-forward routing. When the propagation time of messages through the network is significant, our hybrid algorithms achieve close to optimal performance in terms of phases, intermediate switch settings, and total transmission time. They are the first algorithms to achieve this performance in terms of all three parameters simultaneously.

Broadcast networks of bounded degree

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated ways to construct sparse graphs (networks) in which this process can be completed in minimum time from any originator. The graphs produced by these methods contain high degree vertices. This paper describes graphs with fixed maximum degree in which broadcasting can be completed in near minimum time.

Sparse broadcast graphs

Abstract Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated ways to construct sparse graphs (networks) on n vertices in which this process can be completed in minimum time from any originator. In this paper, we describe four techniques to construct graphs of this type and show that they produce the sparsest known graphs for several values of n . For n = 18, n = 19, n = 30 and n = 31 we also show that our new graphs are minimum broadcast graphs (i.e., that no graph with fewer edges is possible). These new graphs can be used with other techniques to improve the best known results for many larger values of n .

Broadcasting in bounded degree graphs

Broadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. Several previous papers have investigated methods to construct sparse graphs (networks) in which this process can be completed in minimum time from any originator. The graphs produced by these methods contain high degree vertices. [Liestman and Peters, SIAM Journal on Discrete Mathematics, 1 (1988), pp. 531–540 ] and [Bermond and Peyrat, Proceedings of the 19th SE Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, 1988, pp. 283–292] began an investigation of graphs with fixed maximum degree in which broadcasting can be completed in near minimum time. This investigation is continued in this paper by giving lower bounds and constructing bounded degree graphs that allow rapid broadcasting. The constructions use ideas developed by Jerrum and Skyum [IEEE Transactions on Computers, C-...

Evolution and Enhancement of BitTorrent Network Topologies

This paper describes an experimental study that closely examines the underlying topologies of multiple complex networks formed in BitTorrent swarms. Our results demonstrate that the networks exhibit fundamental differences during different stages of a swarm, suggesting that the initial stage is not predictive of the overall performance. We also find a power-law degree distribution in the network of peers that are unchoked by others, which indicates the presence of a robust scale-free network. However, unlike previous studies, we find no clear evidence of persistent clustering in any of the networks, precluding the presence of a small-world that is potentially efficient for peer-to-peer downloading. These results suggest an interesting venue for improving BitTorrents performance. We present a first attempt to introduce clustering into BitTorrent. Our approach is theoretically proven and makes minimal changes to the tracker only. Its effectiveness is verified through a series of simulations and experiments.

Minimum linear gossip graphs and maximal linear (Δ, k)‐gossip graphs

Gossiping is an information dissemination problem in which each node of a communication network has a unique piece of information that must be transmitted to all other nodes using two-way communications between pairs of nodes along the communication links of the network. In this paper, we study gossiping using a linear-cost model of communication which includes a start-up time and a propagation time which is proportional to the amount of information transmitted. A minimum linear gossip graph is a graph (modeling a network), with the minimum possible number of links, in which gossiping can be completed in minimum time under the linear-cost model. For networks with an even number of nodes, we prove that the structure of minimum linear gossip graphs is independent of the relative values of the start-up and unit propagation times. We prove that this is not true when the number of nodes is odd. We present four infinite families of minimum linear gossip graphs. We also present minimum linear gossip graphs for all even numbers of nodes n ≤ 32 except n = 22. A linear (Δ, k)-gossip graph is a graph with maximum degree Δ in which gossiping can be completed in k rounds with minimum propagation time. We present three infinite families of maximal linear (Δ, k)-gossip graphs, that is, linear (Δ, k)-gossip graphs with a maximum number of nodes. We show that not all minimum broadcast graphs are maximal linear (Δ, k)-gossip graphs.

Efficient domination in circulant graphs with two chord lengths

Domination is an important property in the design of efficient computer interconnection networks. We provide a complete characterization of circulant graphs with two chord lengths that admit an efficient dominating set. In particular, for 3-regular and 4-regular circulant graphs, we give necessary and sufficient conditions for the existence of efficient dominating sets and we describe their exact structure according to the relationship between chords.

Energy-aware adaptations in mobile 3d graphics

Smartphone devices are becoming the de facto personal computing platform, rivaling the desktop, as the number of smartphone users is projected to reach 1.1 billion by 2013. Unlike the desktop, smartphones have a constrained energy budget, which is further challenged by increasingly sophisticated applications. Amongst the most popular applications on smartphone devices are games and virtual environments that rely on 3D graphics. Due to the computational intensity of geometry and rasterization, as well as the perpetually illuminated display, these applications are extremely power-hungry. To prolong the battery life of devices running these applications, we propose two new energy-aware adaptation schemes that can be employed in 3D graphics applications: lighting limitation and textural transformation. Our results show that we can conserve between 20% and 33% of energy with acceptable sacrifices to a users visual experience.

Reliable broadcasting

Broadcasting is a process of information dissemination in a communications network whereby a message, originated by one member, is transmitted to all members of the network. By adding some redundant calls to the broadcasting scheme, the completion of the broadcast can be guaranteed in the presence of faulty components. We investigate the implications of transmission failures on broadcasting. In particular, we consider broadcasting when the number of transmission failures is bounded by a constant. We determine the time required to guarantee a broadcast in this model. We also study the number of links required in networks which allow reliable broadcasting.