63,663 research outputs found
Single-machine scheduling with stepwise tardiness costs and release times
We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems
Compressed Genotyping
Significant volumes of knowledge have been accumulated in recent years
linking subtle genetic variations to a wide variety of medical disorders from
Cystic Fibrosis to mental retardation. Nevertheless, there are still great
challenges in applying this knowledge routinely in the clinic, largely due to
the relatively tedious and expensive process of DNA sequencing. Since the
genetic polymorphisms that underlie these disorders are relatively rare in the
human population, the presence or absence of a disease-linked polymorphism can
be thought of as a sparse signal. Using methods and ideas from compressed
sensing and group testing, we have developed a cost-effective genotyping
protocol. In particular, we have adapted our scheme to a recently developed
class of high throughput DNA sequencing technologies, and assembled a
mathematical framework that has some important distinctions from 'traditional'
compressed sensing ideas in order to address different biological and technical
constraints.Comment: Submitted to IEEE Transaction on Information Theory - Special Issue
on Molecular Biology and Neuroscienc
The robust single machine scheduling problem with uncertain release and processing times
In this work, we study the single machine scheduling problem with uncertain
release times and processing times of jobs. We adopt a robust scheduling
approach, in which the measure of robustness to be minimized for a given
sequence of jobs is the worst-case objective function value from the set of all
possible realizations of release and processing times. The objective function
value is the total flow time of all jobs. We discuss some important properties
of robust schedules for zero and non-zero release times, and illustrate the
added complexity in robust scheduling given non-zero release times. We propose
heuristics based on variable neighborhood search and iterated local search to
solve the problem and generate robust schedules. The algorithms are tested and
their solution performance is compared with optimal solutions or lower bounds
through numerical experiments based on synthetic data
Minimizing the average distance to a closest leaf in a phylogenetic tree
When performing an analysis on a collection of molecular sequences, it can be
convenient to reduce the number of sequences under consideration while
maintaining some characteristic of a larger collection of sequences. For
example, one may wish to select a subset of high-quality sequences that
represent the diversity of a larger collection of sequences. One may also wish
to specialize a large database of characterized "reference sequences" to a
smaller subset that is as close as possible on average to a collection of
"query sequences" of interest. Such a representative subset can be useful
whenever one wishes to find a set of reference sequences that is appropriate to
use for comparative analysis of environmentally-derived sequences, such as for
selecting "reference tree" sequences for phylogenetic placement of metagenomic
reads. In this paper we formalize these problems in terms of the minimization
of the Average Distance to the Closest Leaf (ADCL) and investigate algorithms
to perform the relevant minimization. We show that the greedy algorithm is not
effective, show that a variant of the Partitioning Among Medoids (PAM)
heuristic gets stuck in local minima, and develop an exact dynamic programming
approach. Using this exact program we note that the performance of PAM appears
to be good for simulated trees, and is faster than the exact algorithm for
small trees. On the other hand, the exact program gives solutions for all
numbers of leaves less than or equal to the given desired number of leaves,
while PAM only gives a solution for the pre-specified number of leaves. Via
application to real data, we show that the ADCL criterion chooses chimeric
sequences less often than random subsets, while the maximization of
phylogenetic diversity chooses them more often than random. These algorithms
have been implemented in publicly available software.Comment: Please contact us with any comments or questions
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