79,438 research outputs found
Studies of interconnection networks with applications in broadcasting
The exponential growth of interconnection networks transformed the communication primitives into an important area of research. One of these primitives is the one-to-all communication, i.e. broadcasting. Its presence in areas such as static and mobile networks, Internet messaging, supercomputing, multimedia, epidemic algorithms, replicated databases, rumors and virus spreading, to mention only a few, shows the relevance of this primitive. In this thesis we focus on the study of interconnection networks from the perspective of two main problems in broadcasting: the minimum broadcast time problem and the minimum broadcast graph problem. Both problems are discussed under the 1-port constant model, which assumes that each node of the network can communicate with only one other node at a time and the transmitting time is constant, regardless of the size of the message. In the first part we introduce the minimum broadcast time function and we present two new properties of this function. One of the properties yields an iterative heuristic for the minimum broadcast time problem, which is the first iterative approach in approximating the broadcast time of an arbitrary graph. In the second part we give exact upper and lower bounds for the number of broadcast schemes in graphs. We also propose an algorithm for enumerating all the broadcast schemes and a random algorithm for broadcasting. In the third part we present a study of the spectra of Knödel graph and their applications. This study is motivated by the fact that, among the three known infinite families of minimum broadcast graphs, namely the hypercube, the recursive circulant, and the Knödel graph, the last one has the smallest diameter. In the last part we introduce a new measure for the fault tolerance of an interconnection network, which we name the global fault tolerance. Based on this measure, we make a comparative study for the above mentioned classes of minimum broadcast graphs, along with other classes of graphs with good communication properties
Broadcasting with an Energy Harvesting Rechargeable Transmitter
In this paper, we investigate the transmission completion time minimization
problem in a two-user additive white Gaussian noise (AWGN) broadcast channel,
where the transmitter is able to harvest energy from the nature, using a
rechargeable battery. The harvested energy is modeled to arrive at the
transmitter randomly during the course of transmissions. The transmitter has a
fixed number of packets to be delivered to each receiver. Our goal is to
minimize the time by which all of the packets for both users are delivered to
their respective destinations. To this end, we optimize the transmit powers and
transmission rates intended for both users. We first analyze the structural
properties of the optimal transmission policy. We prove that the optimal total
transmit power has the same structure as the optimal single-user transmit
power. We also prove that there exists a cut-off power level for the stronger
user. If the optimal total transmit power is lower than this cut-off level, all
transmit power is allocated to the stronger user, and when the optimal total
transmit power is larger than this cut-off level, all transmit power above this
level is allocated to the weaker user. Based on these structural properties of
the optimal policy, we propose an algorithm that yields the globally optimal
off-line scheduling policy. Our algorithm is based on the idea of reducing the
two-user broadcast channel problem into a single-user problem as much as
possible.Comment: Submitted to IEEE Transactions on Wireless Communications, October
201
Dominating 2-broadcast in graphs: complexity, bounds and extremal graphs
Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded. As a natural extension of domination, we consider dominating 2-broadcasts along with the associated parameter, the dominating 2-broadcast number. We prove that computing the dominating 2-broadcast number is a NP-complete problem, but can be achieved in linear time for trees. We also give an upper bound for this parameter, that is tight for graphs as large as desired.Peer ReviewedPostprint (author's final draft
Optimal Packet Scheduling on an Energy Harvesting Broadcast Link
The minimization of transmission completion time for a given number of bits
per user in an energy harvesting communication system, where energy harvesting
instants are known in an offline manner is considered. An achievable rate
region with structural properties satisfied by the 2-user AWGN Broadcast
Channel capacity region is assumed. It is shown that even though all data are
available at the beginning, a non-negative amount of energy from each energy
harvest is deferred for later use such that the transmit power starts at its
lowest value and rises as time progresses. The optimal scheduler ends the
transmission to both users at the same time. Exploiting the special structure
in the problem, the iterative offline algorithm, FlowRight, from earlier
literature, is adapted and proved to solve this problem. The solution has
polynomial complexity in the number of harvests used, and is observed to
converge quickly on numerical examples.Comment: 25 pages, 6 figures, added lemma and theorems, added reference,
corrected typo
Fairness in Multiuser Systems with Polymatroid Capacity Region
For a wide class of multi-user systems, a subset of capacity region which
includes the corner points and the sum-capacity facet has a special structure
known as polymatroid. Multiaccess channels with fixed input distributions and
multiple-antenna broadcast channels are examples of such systems. Any interior
point of the sum-capacity facet can be achieved by time-sharing among corner
points or by an alternative method known as rate-splitting. The main purpose of
this paper is to find a point on the sum-capacity facet which satisfies a
notion of fairness among active users. This problem is addressed in two cases:
(i) where the complexity of achieving interior points is not feasible, and (ii)
where the complexity of achieving interior points is feasible. For the first
case, the corner point for which the minimum rate of the active users is
maximized (max-min corner point) is desired for signaling. A simple greedy
algorithm is introduced to find the optimum max-min corner point. For the
second case, the polymatroid properties are exploited to locate a rate-vector
on the sum-capacity facet which is optimally fair in the sense that the minimum
rate among all users is maximized (max-min rate). In the case that the rate of
some users can not increase further (attain the max-min value), the algorithm
recursively maximizes the minimum rate among the rest of the users. It is shown
that the problems of deriving the time-sharing coefficients or rate-spitting
scheme can be solved by decomposing the problem to some lower-dimensional
subproblems. In addition, a fast algorithm to compute the time-sharing
coefficients to attain a general point on the sum-capacity facet is proposed.Comment: Submitted To IEEE Transactions on Information Theory, June 200
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
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