10,794 research outputs found
Algorithmic Aspects of a General Modular Decomposition Theory
A new general decomposition theory inspired from modular graph decomposition
is presented. This helps unifying modular decomposition on different
structures, including (but not restricted to) graphs. Moreover, even in the
case of graphs, the terminology ``module'' not only captures the classical
graph modules but also allows to handle 2-connected components, star-cutsets,
and other vertex subsets. The main result is that most of the nice algorithmic
tools developed for modular decomposition of graphs still apply efficiently on
our generalisation of modules. Besides, when an essential axiom is satisfied,
almost all the important properties can be retrieved. For this case, an
algorithm given by Ehrenfeucht, Gabow, McConnell and Sullivan 1994 is
generalised and yields a very efficient solution to the associated
decomposition problem
Pattern overlap implies runaway growth in hierarchical tile systems
We show that in the hierarchical tile assembly model, if there is a
producible assembly that overlaps a nontrivial translation of itself
consistently (i.e., the pattern of tile types in the overlap region is
identical in both translations), then arbitrarily large assemblies are
producible. The significance of this result is that tile systems intended to
controllably produce finite structures must avoid pattern repetition in their
producible assemblies that would lead to such overlap. This answers an open
question of Chen and Doty (SODA 2012), who showed that so-called
"partial-order" systems producing a unique finite assembly *and" avoiding such
overlaps must require time linear in the assembly diameter. An application of
our main result is that any system producing a unique finite assembly is
automatically guaranteed to avoid such overlaps, simplifying the hypothesis of
Chen and Doty's main theorem
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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