10,409 research outputs found
Special cases of online parallel job scheduling
In this paper we consider the online scheduling of jobs, which require processing on a number of machines simultaneously. These jobs are presented to a decision maker one by one, where the next job becomes known as soon as the current job is scheduled. The objective is to minimize the makespan. For the problem with three machines we give a 2.8-competitive algorithm, improving upon the 3-competitive greedy algorithm. For the special case with arbitrary number of machines, where the jobs appear in non-increasing order of machine requirement, we give a 2.4815-competitive algorithm, improving the 2.75-competitive greedy algorithm
Defragmenting the Module Layout of a Partially Reconfigurable Device
Modern generations of field-programmable gate arrays (FPGAs) allow for
partial reconfiguration. In an online context, where the sequence of modules to
be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of
modules leads to progressive fragmentation of the available space, making
defragmentation an important issue. We address this problem by propose an
online and an offline component for the defragmentation of the available space.
We consider defragmenting the module layout on a reconfigurable device. This
corresponds to solving a two-dimensional strip packing problem. Problems of
this type are NP-hard in the strong sense, and previous algorithmic results are
rather limited. Based on a graph-theoretic characterization of feasible
packings, we develop a method that can solve two-dimensional defragmentation
instances of practical size to optimality. Our approach is validated for a set
of benchmark instances.Comment: 10 pages, 11 figures, 1 table, Latex, to appear in "Engineering of
Reconfigurable Systems and Algorithms" as a "Distinguished Paper
Power Strip Packing of Malleable Demands in Smart Grid
We consider a problem of supplying electricity to a set of
customers in a smart-grid framework. Each customer requires a certain amount of
electrical energy which has to be supplied during the time interval . We
assume that each demand has to be supplied without interruption, with possible
duration between and , which are given system parameters (). At each moment of time, the power of the grid is the sum of all the
consumption rates for the demands being supplied at that moment. Our goal is to
find an assignment that minimizes the {\it power peak} - maximal power over
- while satisfying all the demands. To do this first we find the lower
bound of optimal power peak. We show that the problem depends on whether or not
the pair belongs to a "good" region . If it does - then
an optimal assignment almost perfectly "fills" the rectangle with being the sum of all the energy demands - thus
achieving an optimal power peak . Conversely, if do not belong to
, we identify the lower bound on the optimal value of
power peak and introduce a simple linear time algorithm that almost perfectly
arranges all the demands in a rectangle
and show that it is asymptotically optimal
Online Circle and Sphere Packing
In this paper we consider the Online Bin Packing Problem in three variants:
Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes.
The two first ones receive an online sequence of circles (items) of different
radii while the third one receive an online sequence of spheres (items) of
different radii, and they want to pack the items into the minimum number of
unit squares, isosceles right triangles of leg length one, and unit cubes,
respectively. For Online Circle Packing in Squares, we improve the previous
best-known competitive ratio for the bounded space version, when at most a
constant number of bins can be open at any given time, from 2.439 to 2.3536.
For Online Circle Packing in Isosceles Right Triangles and Online Sphere
Packing in Cubes we show bounded space algorithms of asymptotic competitive
ratios 2.5490 and 3.5316, respectively, as well as lower bounds of 2.1193 and
2.7707 on the competitive ratio of any online bounded space algorithm for these
two problems. We also considered the online unbounded space variant of these
three problems which admits a small reorganization of the items inside the bin
after their packing, and we present algorithms of competitive ratios 2.3105,
2.5094, and 3.5146 for Circles in Squares, Circles in Isosceles Right
Triangles, and Spheres in Cubes, respectively
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