190 research outputs found
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
Steiner Distance in Product Networks
For a connected graph of order at least and , the
\emph{Steiner distance} among the vertices of is the minimum size
among all connected subgraphs whose vertex sets contain . Let and be
two integers with . Then the \emph{Steiner -eccentricity
} of a vertex of is defined by . Furthermore, the
\emph{Steiner -diameter} of is . In this paper, we investigate the Steiner distance and Steiner
-diameter of Cartesian and lexicographical product graphs. Also, we study
the Steiner -diameter of some networks.Comment: 29 pages, 4 figure
Broadcasting in Harary Graphs
With the increasing popularity of interconnection networks, efficient information dissemination has become a popular research area. Broadcasting is one of the information dissemination primitives. Broadcasting in a graph is the process of transmitting a message from one vertex, the originator, to all other vertices of the graph. We follow the classical model for broadcasting.
This thesis studies the Harary graph in depth. First, we find the diameter of Harary graph. We present an additive approximation algorithm for the broadcast problem in Harary graph. We also provide some properties for the graph like vertex transitivity, circulant graph and regularity.
In the next part we introduce modified harary graph. We calculate the diameter and broadcast time for the graph. We will also provide 1-additive approximation algorithm to find the broadcast time in the modified harary graph
Hybrid Dissemination: Adding Determinism to Probabilistic Multicasting in Large-Scale P2P Systems
Abstract. Epidemic protocols have demonstrated remarkable scalability and robustness in disseminating information on internet-scale, dynamic P2P systems. However, popular instances of such protocols suffer from a number of significant drawbacks, such as increased message overhead in push-based systems, or low dissemination speed in pull-based ones. In this paper we study push-based epidemic dissemination algorithms, in terms of hit ratio, communication overhead, dissemination speed, and resilience to failures and node churn. We devise a hybrid push-based dissemination algorithm, combining probabilistic with deterministic properties, which limits message overhead to an order of magnitude lower than that of the purely probabilistic dissemination model, while retaining strong probabilistic guarantees for complete dissemination of messages. Our extensive experimentation shows that our proposed algorithm outperforms that model both in static and dynamic network scenarios, as well as in the face of large-scale catastrophic failures. Moreover, the proposed algorithm distributes the dissemination load uniformly on all participating nodes. Keywords: Epidemic/Gossip protocols, Information Dissemination, Peer-to-Peer
Multi-hop Byzantine reliable broadcast with honest dealer made practical
We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g., digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment
On (t,r) Broadcast Domination Numbers of Grids
The domination number of a graph is the minimum cardinality of
any subset such that every vertex in is in or adjacent to
an element of . Finding the domination numbers of by grids was an
open problem for nearly 30 years and was finally solved in 2011 by Goncalves,
Pinlou, Rao, and Thomass\'e. Many variants of domination number on graphs have
been defined and studied, but exact values have not yet been obtained for
grids. We will define a family of domination theories parameterized by pairs of
positive integers where which generalize domination
and distance domination theories for graphs. We call these domination numbers
the broadcast domination numbers. We give the exact values of
broadcast domination numbers for small grids, and we identify upper bounds for
the broadcast domination numbers for large grids and conjecture that
these bounds are tight for sufficiently large grids.Comment: 28 pages, 43 figure
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