5,042 research outputs found
On three soft rectangle packing problems with guillotine constraints
We investigate how to partition a rectangular region of length and
height into rectangles of given areas using
two-stage guillotine cuts, so as to minimize either (i) the sum of the
perimeters, (ii) the largest perimeter, or (iii) the maximum aspect ratio of
the rectangles. These problems play an important role in the ongoing Vietnamese
land-allocation reform, as well as in the optimization of matrix multiplication
algorithms. We show that the first problem can be solved to optimality in
, while the two others are NP-hard. We propose mixed
integer programming (MIP) formulations and a binary search-based approach for
solving the NP-hard problems. Experimental analyses are conducted to compare
the solution approaches in terms of computational efficiency and solution
quality, for different objectives
Comparing several heuristics for a packing problem
Packing problems are in general NP-hard, even for simple cases. Since now
there are no highly efficient algorithms available for solving packing
problems. The two-dimensional bin packing problem is about packing all given
rectangular items, into a minimum size rectangular bin, without overlapping.
The restriction is that the items cannot be rotated. The current paper is
comparing a greedy algorithm with a hybrid genetic algorithm in order to see
which technique is better for the given problem. The algorithms are tested on
different sizes data.Comment: 5 figures, 2 tables; accepted: International Journal of Advanced
Intelligence Paradigm
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
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