243 research outputs found
Makespan Scheduling of Unit Jobs with Precedence Constraints in time
In a classical scheduling problem, we are given a set of jobs of unitlength along with precedence constraints and the goal is to find a schedule ofthese jobs on identical machines that minimizes the makespan. This problemis well-known to be NP-hard for an unbounded number of machines. Using standard3-field notation, it is known as . We present an algorithm for this problem that runs in time.Before our work, even for machines the best known algorithms ran in time. In contrast, our algorithm works when the number ofmachines is unbounded. A crucial ingredient of our approach is an algorithmwith a runtime that is only single-exponential in the vertex cover of thecomparability graph of the precedence constraint graph. This heavily relies oninsights from a classical result by Dolev and Warmuth (Journal of Algorithms1984) for precedence graphs without long chains.<br
Makespan Scheduling of Unit Jobs with Precedence Constraints in time
In a classical scheduling problem, we are given a set of jobs of unit
length along with precedence constraints and the goal is to find a schedule of
these jobs on identical machines that minimizes the makespan. This problem
is well-known to be NP-hard for an unbounded number of machines. Using standard
3-field notation, it is known as .
We present an algorithm for this problem that runs in time.
Before our work, even for machines the best known algorithms ran in
time. In contrast, our algorithm works when the number of
machines is unbounded. A crucial ingredient of our approach is an algorithm
with a runtime that is only single-exponential in the vertex cover of the
comparability graph of the precedence constraint graph. This heavily relies on
insights from a classical result by Dolev and Warmuth (Journal of Algorithms
1984) for precedence graphs without long chains.Comment: 26 pages, 7 figure
Parameterized Complexities of Dominating and Independent Set Reconfiguration
We settle the parameterized complexities of several variants of independent
set reconfiguration and dominating set reconfiguration, parameterized by the
number of tokens. We show that both problems are XL-complete when there is no
limit on the number of moves and XNL-complete when a maximum length for
the sequence is given in binary in the input. The problems are known to be
XNLP-complete when is given in unary instead, and - and
-hard respectively when is also a parameter. We complete the
picture by showing membership in those classes.
Moreover, we show that for all the variants that we consider, token sliding
and token jumping are equivalent under pl-reductions. We introduce partitioned
variants of token jumping and token sliding, and give pl-reductions between the
four variants that have precise control over the number of tokens and the
length of the reconfiguration sequence.Comment: 31 pages, 3 figure
The influence of inhomogeneities on the cardiac-magnetic-field distribution
Numerical computations were performed on the magnetic field generated by the heart during ventricular depolarization. The purpose of this study was to investigate the contribution of inhomogeneities in the volume conductor to the total field and to establish the influence of gradiometers as used in experimental recordings
BISON ontwerpgerichte evaluatie:criteria, indicatoren en instrumenten
Deze deliverable van het BISON project beschrijft de criteria en instrumenten die gebruikt zijn in de (formatieve) evaluatie van drie scenario's voor samenwerkend leren in de virtuele klas
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