58 research outputs found
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
Models and algorithms for energy-efficient scheduling with immediate start of jobs
We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlogn) time in the single-machine case and in O(n²m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution
On the Hitting Set of Bundles Problem
Le problème de l'ensemble minimal de paquets (minimal hitting set of bundles problem ou HSB) est défini comme suit. On dispose d'un ensemble E = {e1, e2, . . . , en} de n éléments. Chaque élément ei (i = 1, . . . , n) a un coût positif ou nul ci. Un paquet b est un sous ensemble de E. On dispose aussi d'une collection S = {S1, S2, . . . , Sm} de m ensembles de paquets. De manière plus précise, chaque ensemble Sj (j = 1, . . . ,m) est composé de g(j) paquets distincts notés b1j , b2j , . . . , bg(j) j . Une solution du problème HSB est un sous ensemble E0 E tel que pour tout Sj 2 S, au moins un paquet est couvert, i.e. bl j E0. Le coût total de la solution, noté C(E0), est P{i|ei2E0} ci. Le problème consiste à trouver une solution de coût total minimum. Nous donnons un algorithme déterministe N(1 − (1 − 1 N )M)-approché, où N est le nombre maximal de paquets par ensemble etM est le nombre maximal d'ensembles à qui un élément appartient. Le rapport d'approximation est à peu de choses près le meilleur que l'on puisse proposer car on peut montrer que HSB ne peut être approché avec un rapport 7/6 − lorsque N = 2 et N − 1 − lorsque N 3. L'algorithme proposé est aussi le premier offrant une garantie de performance pour le problème classique d'optimisation de requêtes multiples [9, 10]. Son rapport d'approximation pour le problème MIN k−SAT dont il est une généralisation est le même que celui du meilleur algorithme connu [3]
On the parallel complexity of the alternating Hamiltonian cycle problem
Given a graph with colored edges, a Hamiltonian cycle is
called alternating if its successive edges differ in color. The problem
of finding such a cycle, even for 2-edge-colored graphs, is trivially
NP-complete, while it is known to be polynomial for 2-edge-colored
complete graphs. In this paper we study the parallel complexity of
finding such a cycle, if any, in 2-edge-colored complete graphs. We give
a new characterization for such a graph admitting an alternating
Hamiltonian cycle which allows us to derive a parallel algorithm for
the problem. Our parallel solution uses a perfect matching algorithm
putting the alternating Hamiltonian cycle problem to the RNC class. In
addition, a sequential version of our parallel algorithm improves the
computation time of the fastest known sequential algorithm for the
alternating Hamiltonian cycle problem by a factor of
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