5 research outputs found
A survey of offline algorithms for energy minimization under deadline constraints
Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
On a reduction for a class of resource allocation problems
In the resource allocation problem (RAP), the goal is to divide a given
amount of resource over a set of activities while minimizing the cost of this
allocation and possibly satisfying constraints on allocations to subsets of the
activities. Most solution approaches for the RAP and its extensions allow each
activity to have its own cost function. However, in many applications, often
the structure of the objective function is the same for each activity and the
difference between the cost functions lies in different parameter choices such
as, e.g., the multiplicative factors. In this article, we introduce a new class
of objective functions that captures the majority of the objectives occurring
in studied applications. These objectives are characterized by a shared
structure of the cost function depending on two input parameters. We show that,
given the two input parameters, there exists a solution to the RAP that is
optimal for any choice of the shared structure. As a consequence, this problem
reduces to the quadratic RAP, making available the vast amount of solution
approaches and algorithms for the latter problem. We show the impact of our
reduction result on several applications and, in particular, we improve the
best known worst-case complexity bound of two important problems in vessel
routing and processor scheduling from to