Analysis of peer-to-peer file dissemination

In recent years, overlay networks have proven a popular way of disseminating potentially large files from a single server S to a potentially large group of N end users via the Internet. A number of algorithms and protocols have been suggested, implemented and studied. In particular, much attention has been given to peer-to-peer (P2P) systems such as BitTorrent, Slurpie, SplitStream, Bullet and Avalanche. The key idea is that the file is divided into M parts of equal size and that a given user may download any one of these -- or, for Avalanche, linear combinations of these -- either from the server or from a peer who has previously downloaded it. However, performance analysis of P2P systems for file dissemination has typically been limited to comparing one system relative to another and typically been realized by means of simulations and measurements. We give the minimal time to fully disseminate the file of M parts from a server to N end users in a centralized scenario. In the scheduling literature this completion time is referred to as makespan. We thereby provide a lower bound which can be used as a performance benchmark for any P2P file dissemination system. We also investigate the part of the loss in efficiency that is due to the lack of centralized control in practice. Using simulation as well as direct computation, we show that even a simple and natural randomized strategy disseminates the file in an expected time that grows with N in a similar manner to the minimal time achieved with a centralized controller. This suggests that the performance of necessarily decentralized P2P file dissemination systems should still be close to our performance bound

Multiple message broadcasting and gossiping in the dynamically orientable graphs

This research investigates the problems of gossiping and multiple message broadcasting in dynamically orientable graphs of different network topologies. These are new problems never attempted before. Dynamically orientable graphs and six different network topologies are considered: paths, cycles, stars, binary trees, complete trees and two-dimensional grids. Information dissemination in graphs that are dynamically orientable requires that number of messages sent in each direction along an edge be balanced and therefore necessitates a different approach in gossiping and multiple message broadcasting.;The obvious upper bound for gossiping and multiple message broadcasting in dynamically orientable graphs is twice the best known time for gossiping and multiple message broadcasting in classical graphs. This is obtained by inserting an additional time step t\u27 after each time step t in the classical graph algorithm in which all calls of time step t are repeated with messages moving along the same edges but in the opposite direction to reset the bias of these edges. Finding better bounds for gossiping and multiple message broadcasting in dynamically orientable graphs is the goal of this research.;For each network topology an algorithm is proposed to perform gossiping and multiple message broadcasting. For some network topologies proposed algorithms for dynamically orientable graphs achieved the same upper bound as it is known for classical graphs, for example, gossiping in dynamically orientable grid graphs. In some cases the best time is the twice the best known time for gossiping and multiple message broadcasting in classical graphs, for example, gossiping in dynamically orientable star graphs. In other cases, good time bounds are achieved that are very close to the upper bounds in classical graphs, for example, multiple message broadcasting in dynamically orientable grid graphs. Multiple message broadcasting in dynamically orientable cycle graphs is also a good example of close upper bounds. As number of messages increases bounds become very close to each other

Optimal broadcasting in treelike graphs

Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator , disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Once informed, the nodes aid the originator in distributing the message. Finding the broadcast time of a vertex in an arbitrary graph is NP-complete. The problem is solved polynomially only for a few classes of graphs. In this thesis we study the broadcast problem in different classes of graphs which have various similarities to trees. The unicyclic graph is the simplest graph family after trees, it is a connected graph with only one cycle in it. We provide a linear time solution for the broadcast problem in unicyclic graphs. We also studied graphs with increasing number of cycles and complexity and provide again polynomial time solutions. These graph families are: tree of cycles, necklace graphs, and 2-restricted cactus graphs. We also define the fully connected tree graphs and provide a polynomial solution and use these results to obtain polynomial solution for the broadcast problem in tree of cliques and a constant approximation algorithm for the hierarchical tree cluster networks

Approximation Algorithms for Broadcasting in Simple Graphs with Intersecting Cycles

Broadcasting is an information dissemination problem in a connected network in which one node, called the originator, must distribute a message to all other nodes by placing a series of calls along the communication lines of the network. Every time the informed nodes aid the originator in distributing the message. Finding the minimum broadcast time of any vertex in an arbitrary graph is NP-Complete. The problem remains NP-Complete even for planar graphs of degree 3 and for a graph whose vertex set can be partitioned into a clique and an independent set. The best theoretical upper bound gives logarithmic approximation. It has been shown that the broadcasting problem is NP-Hard to approximate within a factor of 3-ɛ. The polynomial time solvability is shown only for tree-like graphs; trees, unicyclic graphs, tree of cycles, necklace graphs and some graphs where the underlying graph is a clique; such as fully connected trees and tree of cliques. In this thesis we study the broadcast problem in different classes of graphs where cycles intersect in at least one vertex. First we consider broadcasting in a simple graph where several cycles have common paths and two intersecting vertices, called a k-path graph. We present a constant approximation algorithm to find the broadcast time of an arbitrary k-path graph. We also study the broadcast problem in a simple cactus graph called k-cycle graph where several cycles of arbitrary lengths are connected by a central vertex on one end. We design a constant approximation algorithm to find the broadcast time of an arbitrary k-cycle graph. Next we study the broadcast problem in a hypercube of trees for which we present a 2-approximation algorithm for any originator. We provide a linear algorithm to find the broadcast time in hypercube of trees with one tree. We extend the result for any arbitrary graph whose nodes contain trees and design a linear time constant approximation algorithm where the broadcast scheme in the arbitrary graph is already known. In Chapter 6 we study broadcasting in Harary graph for which we present an additive approximation which gives 2-approximation in the worst case to find the broadcast time in an arbitrary Harary graph. Next for even values of n, we introduce a new graph, called modified-Harary graph and present a 1-additive approximation algorithm to find the broadcast time. We also show that a modified-Harary graph is a broadcast graph when k is logarithmic of n. Finally we consider a diameter broadcast problem where we obtain a lower bound on the broadcast time of the graph which has at least (d+k-1 choose d) + 1 vertices that are at a distance d from the originator, where k >= 1