6,012 research outputs found
Throughput Maximization in the Speed-Scaling Setting
We are given a set of jobs and a single processor that can vary its speed
dynamically. Each job is characterized by its processing requirement
(work) , its release date and its deadline . We are also given
a budget of energy and we study the scheduling problem of maximizing the
throughput (i.e. the number of jobs which are completed on time). We propose a
dynamic programming algorithm that solves the preemptive case of the problem,
i.e. when the execution of the jobs may be interrupted and resumed later, in
pseudo-polynomial time. Our algorithm can be adapted for solving the weighted
version of the problem where every job is associated with a weight and
the objective is the maximization of the sum of the weights of the jobs that
are completed on time. Moreover, we provide a strongly polynomial time
algorithm to solve the non-preemptive unweighed case when the jobs have the
same processing requirements. For the weighted case, our algorithm can be
adapted for solving the non-preemptive version of the problem in
pseudo-polynomial time.Comment: submitted to SODA 201
Throughput Maximization in Multiprocessor Speed-Scaling
We are given a set of jobs that have to be executed on a set of
speed-scalable machines that can vary their speeds dynamically using the energy
model introduced in [Yao et al., FOCS'95]. Every job is characterized by
its release date , its deadline , its processing volume if
is executed on machine and its weight . We are also given a budget
of energy and our objective is to maximize the weighted throughput, i.e.
the total weight of jobs that are completed between their respective release
dates and deadlines. We propose a polynomial-time approximation algorithm where
the preemption of the jobs is allowed but not their migration. Our algorithm
uses a primal-dual approach on a linearized version of a convex program with
linear constraints. Furthermore, we present two optimal algorithms for the
non-preemptive case where the number of machines is bounded by a fixed
constant. More specifically, we consider: {\em (a)} the case of identical
processing volumes, i.e. for every and , for which we
present a polynomial-time algorithm for the unweighted version, which becomes a
pseudopolynomial-time algorithm for the weighted throughput version, and {\em
(b)} the case of agreeable instances, i.e. for which if and only
if , for which we present a pseudopolynomial-time algorithm. Both
algorithms are based on a discretization of the problem and the use of dynamic
programming
Wireless MIMO Switching: Weighted Sum Mean Square Error and Sum Rate Optimization
This paper addresses joint transceiver and relay design for a wireless
multiple-input-multiple-output (MIMO) switching scheme that enables data
exchange among multiple users. Here, a multi-antenna relay linearly precodes
the received (uplink) signals from multiple users before forwarding the signal
in the downlink, where the purpose of precoding is to let each user receive its
desired signal with interference from other users suppressed. The problem of
optimizing the precoder based on various design criteria is typically
non-convex and difficult to solve. The main contribution of this paper is a
unified approach to solve the weighted sum mean square error (MSE) minimization
and weighted sum rate maximization problems in MIMO switching. Specifically, an
iterative algorithm is proposed for jointly optimizing the relay's precoder and
the users' receive filters to minimize the weighted sum MSE. It is also shown
that the weighted sum rate maximization problem can be reformulated as an
iterated weighted sum MSE minimization problem and can therefore be solved
similarly to the case of weighted sum MSE minimization. With properly chosen
initial values, the proposed iterative algorithms are asymptotically optimal in
both high and low signal-to-noise ratio (SNR) regimes for MIMO switching,
either with or without self-interference cancellation (a.k.a., physical-layer
network coding). Numerical results show that the optimized MIMO switching
scheme based on the proposed algorithms significantly outperforms existing
approaches in the literature.Comment: This manuscript is under 2nd review of IEEE Transactions on
Information Theor
Heterogeneous Congestion Control: Efficiency, Fairness and Design
When heterogeneous congestion control protocols that react to different pricing signals (e.g. packet loss, queueing delay, ECN marking etc.) share the same network, the current theory based on utility maximization fails to predict the network behavior. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, inefficient and unfair. This paper has two objectives. First, we demonstrate the intricate behaviors of a heterogeneous network through simulations and present a rigorous framework to help understand its equilibrium efficiency and fairness properties. By identifying an optimization problem associated with every equilibrium, we show that every equilibrium is Pareto efficient and provide an upper bound on efficiency loss due to pricing heterogeneity. On fairness, we show that intra-protocol fairness is still decided by a utility maximization problem while inter-protocol fairness is the part over which we don¿t have control. However it is shown that we can achieve any desirable inter-protocol fairness by properly choosing protocol parameters. Second, we propose a simple slow timescale source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns and prove its feasibility. The scheme needs only local information
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