3,532 research outputs found
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
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
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
Closing the Gap for Pseudo-Polynomial Strip Packing
Two-dimensional packing problems are a fundamental class of optimization problems and Strip Packing is one of the most natural and famous among them. Indeed it can be defined in just one sentence: Given a set of rectangular axis parallel items and a strip with bounded width and infinite height, the objective is to find a packing of the items into the strip minimizing the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known that there is no pseudo-polynomial time algorithm for Strip Packing with a ratio better than 5/4 unless P = NP. The best algorithm so far has a ratio of 4/3 + epsilon. In this paper, we close the gap between inapproximability result and currently known algorithms by presenting an algorithm with approximation ratio 5/4 + epsilon. The algorithm relies on a new structural result which is the main accomplishment of this paper. It states that each optimal solution can be transformed with bounded loss in the objective such that it has one of a polynomial number of different forms thus making the problem tractable by standard techniques, i.e., dynamic programming. To show the conceptual strength of the approach, we extend our result to other problems as well, e.g., Strip Packing with 90 degree rotations and Contiguous Moldable Task Scheduling, and present algorithms with approximation ratio 5/4 + epsilon for these problems as well
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
We study the Parallel Task Scheduling problem with a
constant number of machines. This problem is known to be strongly NP-complete
for each , while it is solvable in pseudo-polynomial time for each . We give a positive answer to the long-standing open question whether
this problem is strongly -complete for . As a second result, we
improve the lower bound of for approximating pseudo-polynomial
Strip Packing to . Since the best known approximation algorithm
for this problem has a ratio of , this result
narrows the gap between approximation ratio and inapproximability result by a
significant step. Both results are proven by a reduction from the strongly
-complete problem 3-Partition
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