49,688 research outputs found
Data Exchange Problem with Helpers
In this paper we construct a deterministic polynomial time algorithm for the
problem where a set of users is interested in gaining access to a common file,
but where each has only partial knowledge of the file. We further assume the
existence of another set of terminals in the system, called helpers, who are
not interested in the common file, but who are willing to help the users. Given
that the collective information of all the terminals is sufficient to allow
recovery of the entire file, the goal is to minimize the (weighted) sum of bits
that these terminals need to exchange over a noiseless public channel in order
achieve this goal. Based on established connections to the multi-terminal
secrecy problem, our algorithm also implies a polynomial-time method for
constructing the largest shared secret key in the presence of an eavesdropper.
We consider the following side-information settings: (i) side-information in
the form of uncoded packets of the file, where the terminals' side-information
consists of subsets of the file; (ii) side-information in the form of linearly
correlated packets, where the terminals have access to linear combinations of
the file packets; and (iii) the general setting where the the terminals'
side-information has an arbitrary (i.i.d.) correlation structure. We provide a
polynomial-time algorithm (in the number of terminals) that finds the optimal
rate allocations for these terminals, and then determines an explicit optimal
transmission scheme for cases (i) and (ii)
Non-Cooperative Scheduling of Multiple Bag-of-Task Applications
Multiple applications that execute concurrently on heterogeneous platforms
compete for CPU and network resources. In this paper we analyze the behavior of
non-cooperative schedulers using the optimal strategy that maximize their
efficiency while fairness is ensured at a system level ignoring applications
characteristics. We limit our study to simple single-level master-worker
platforms and to the case where each scheduler is in charge of a single
application consisting of a large number of independent tasks. The tasks of a
given application all have the same computation and communication requirements,
but these requirements can vary from one application to another. In this
context, we assume that each scheduler aims at maximizing its throughput. We
give closed-form formula of the equilibrium reached by such a system and study
its performance. We characterize the situations where this Nash equilibrium is
optimal (in the Pareto sense) and show that even though no catastrophic
situation (Braess-like paradox) can occur, such an equilibrium can be
arbitrarily bad for any classical performance measure
On Resource Allocation in Fading Multiple Access Channels - An Efficient Approximate Projection Approach
We consider the problem of rate and power allocation in a multiple-access
channel. Our objective is to obtain rate and power allocation policies that
maximize a general concave utility function of average transmission rates on
the information theoretic capacity region of the multiple-access channel. Our
policies does not require queue-length information. We consider several
different scenarios. First, we address the utility maximization problem in a
nonfading channel to obtain the optimal operating rates, and present an
iterative gradient projection algorithm that uses approximate projection. By
exploiting the polymatroid structure of the capacity region, we show that the
approximate projection can be implemented in time polynomial in the number of
users. Second, we consider resource allocation in a fading channel. Optimal
rate and power allocation policies are presented for the case that power
control is possible and channel statistics are available. For the case that
transmission power is fixed and channel statistics are unknown, we propose a
greedy rate allocation policy and provide bounds on the performance difference
of this policy and the optimal policy in terms of channel variations and
structure of the utility function. We present numerical results that
demonstrate superior convergence rate performance for the greedy policy
compared to queue-length based policies. In order to reduce the computational
complexity of the greedy policy, we present approximate rate allocation
policies which track the greedy policy within a certain neighborhood that is
characterized in terms of the speed of fading.Comment: 32 pages, Submitted to IEEE Trans. on Information Theor
Derandomization of Online Assignment Algorithms for Dynamic Graphs
This paper analyzes different online algorithms for the problem of assigning
weights to edges in a fully-connected bipartite graph that minimizes the
overall cost while satisfying constraints. Edges in this graph may disappear
and reappear over time. Performance of these algorithms is measured using
simulations. This paper also attempts to derandomize the randomized online
algorithm for this problem
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