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In this paper, we study the problem of makespan minimization for the multiprocessor
scheduling problem in the presence of communication delays. The communication delay
between two tasks i and j depends on the distance
between the two processors on which these two tasks are executed. Lahlou shows that a
simple polynomial-time algorithm exists when the length of the schedule is at most two
(the problem becomes 𝒩𝒫-complete when the length of the schedule
...
In this paper, we study the problem of makespan minimization for the multiprocessor
scheduling problem in the presence of communication delays. The communication delay
between two tasks i and j depends on the distance
between the two processors on which these two tasks are executed. Lahlou shows that a
simple polynomial-time algorithm exists when the length of the schedule is at most two
(the problem becomes 𝒩𝒫-complete when the length of the schedule
...
We study matrix calculations such as diagonalization of quadratic forms under the aspect of additive complexity and relate these complexities to the complexity of matrix multiplication. While in Bürgisser et al. (1991) for multiplicative complexity the customary thick path existence argument was sufficient, here for additive complexity we need the more delicate finess of the real spectrum (cf. Bochnak et al. (1987), Becker (1986), Knebusch and Scheiderer (1989)) to obtain a complexity relativization....
An exact analysis is given of the benefits of using the non-adjacent form representation for integers (rather than the binary representation), when computing powers of elements in a group in which inverting is easy. By counting the number of multiplications for a random exponent requiring a given number of bits in its binary representation, we arrive at a precise version of the known asymptotic result that on average one in three signed bits in the non-adjacent form is non-zero. This shows that...
Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...
Cover automata for finite languages have been much studied a few years ago.
It turns out that a simple mathematical structure, namely
similarity relations over a finite set of words, is underlying these
studies. In the present work, we investigate in detail for themselves
the properties of these relations beyond the scope of finite languages.
New results with straightforward proofs
are obtained in this generalized framework,
and previous results concerning cover
automata are obtained as immediate...
We present the combination of a state control and shape design approaches for the optimization of micro-fluidic channels used for sample extraction and separation of chemical species existing in a buffer solution. The aim is to improve the extraction and identification capacities of electroosmotic micro-fluidic devices by avoiding dispersion of the extracted advected band.
We present the combination of a state control and shape design approaches
for the optimization of micro-fluidic channels used for sample extraction and
separation of chemical species existing in a buffer solution.
The aim is to improve the extraction and identification capacities of
electroosmotic micro-fluidic devices by avoiding dispersion of the
extracted advected band.
Let be a field whose characteristic is not and . We give a simple algorithm to find, given , a nontrivial solution in (if it exists) to the equation . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in ; hence we obtain a recursive algorithm for solving diagonal conics over (using existing algorithms for such equations over ) and over .
We propose a heuristic for solving the maximum independent set
problem for a set of processors in a network with arbitrary
topology. We assume an asynchronous model of computation and we use
modified Hopfield neural networks to find high quality solutions. We
analyze the algorithm in terms of the number of rounds necessary to
find admissible solutions both in the worst case (theoretical
analysis) and in the average case (experimental Analysis). We show
that our heuristic is better than the...
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