12,800 research outputs found
Complexity dichotomy on partial grid recognition
Deciding whether a graph can be embedded in a grid using only unit-length
edges is NP-complete, even when restricted to binary trees. However, it is not
difficult to devise a number of graph classes for which the problem is
polynomial, even trivial. A natural step, outstanding thus far, was to provide
a broad classification of graphs that make for polynomial or NP-complete
instances. We provide such a classification based on the set of allowed vertex
degrees in the input graphs, yielding a full dichotomy on the complexity of the
problem. As byproducts, the previous NP-completeness result for binary trees
was strengthened to strictly binary trees, and the three-dimensional version of
the problem was for the first time proven to be NP-complete. Our results were
made possible by introducing the concepts of consistent orientations and robust
gadgets, and by showing how the former allows NP-completeness proofs by local
replacement even in the absence of the latter
A partitioning strategy for nonuniform problems on multiprocessors
The partitioning of a problem on a domain with unequal work estimates in different subddomains is considered in a way that balances the work load across multiple processors. Such a problem arises for example in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. A binary decomposition of the domain is used to partition it into rectangles requiring equal computational effort. The communication costs of mapping this partitioning onto different microprocessors: a mesh-connected array, a tree machine and a hypercube is then studied. The communication cost expressions can be used to determine the optimal depth of the above partitioning
Methods and problems of wavelength-routing in all-optical networks
We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions
Tight Bounds for On-line Tree Embedding
Many tree–structured computations are inherently parallel.
As leaf processes are recursively spawned they can
be assigned to independent processors in a multicomputer
network. To maintain load balance, an on–line
mapping algorithm must distribute processes equitably
among processors. Additionally, the algorithm itself
must be distributed in nature, and process allocation
must be completed via message–passing with minimal
communication overhead.
This paper investigates bounds on the performance
of deterministic and randomized algorithms for on–line
tree embedding. In particular, we study tradeoffs between
performance (load–balance) and communication
overhead (message congest ion). We give a simple technique
to derive lower bounds on the congestion that
any on–line allocation algorithm must incur in order to
guarantee load balance. This technique works for both
randomized and deterministic algorithms, although we
find that the performance of randomized on-line algorithms
to be somewhat better than that of deterministic
algorithms. Optimal bounds are achieved for several
networks including multi–dimensional grids and butterflies
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