401 research outputs found
Single machine scheduling with job-dependent machine deterioration
We consider the single machine scheduling problem with job-dependent machine
deterioration. In the problem, we are given a single machine with an initial
non-negative maintenance level, and a set of jobs each with a non-preemptive
processing time and a machine deterioration. Such a machine deterioration
quantifies the decrement in the machine maintenance level after processing the
job. To avoid machine breakdown, one should guarantee a non-negative
maintenance level at any time point; and whenever necessary, a maintenance
activity must be allocated for restoring the machine maintenance level. The
goal of the problem is to schedule the jobs and the maintenance activities such
that the total completion time of jobs is minimized. There are two variants of
maintenance activities: in the partial maintenance case each activity can be
allocated to increase the machine maintenance level to any level not exceeding
the maximum; in the full maintenance case every activity must be allocated to
increase the machine maintenance level to the maximum. In a recent work, the
problem in the full maintenance case has been proven NP-hard; several special
cases of the problem in the partial maintenance case were shown solvable in
polynomial time, but the complexity of the general problem is left open. In
this paper we first prove that the problem in the partial maintenance case is
NP-hard, thus settling the open problem; we then design a -approximation
algorithm.Comment: 15 page
Planar graphs are acyclically edge -colorable
An edge coloring of a graph is to color all the edges in the graph such
that adjacent edges receive different colors. It is acyclic if each cycle in
the graph receives at least three colors. Fiam{\v{c}}ik (1978) and Alon,
Sudakov and Zaks (2001) conjectured that every simple graph with maximum degree
is acyclically edge -colorable -- the well-known acyclic
edge coloring conjecture (AECC). Despite many major breakthroughs and minor
improvements, the conjecture remains open even for planar graphs. In this
paper, we prove that planar graphs are acyclically edge -colorable. Our proof has two main steps: Using discharging methods, we
first show that every non-trivial planar graph must have one of the eight
groups of well characterized local structures; and then acyclically edge color
the graph using no more than colors by an induction on the number
of edges.Comment: Full version with 120 page
A stable gene selection in microarray data analysis
BACKGROUND: Microarray data analysis is notorious for involving a huge number of genes compared to a relatively small number of samples. Gene selection is to detect the most significantly differentially expressed genes under different conditions, and it has been a central research focus. In general, a better gene selection method can improve the performance of classification significantly. One of the difficulties in gene selection is that the numbers of samples under different conditions vary a lot. RESULTS: Two novel gene selection methods are proposed in this paper, which are not affected by the unbalanced sample class sizes and do not assume any explicit statistical model on the gene expression values. They were evaluated on eight publicly available microarray datasets, using leave-one-out cross-validation and 5-fold cross-validation. The performance is measured by the classification accuracies using the top ranked genes based on the training datasets. CONCLUSION: The experimental results showed that the proposed gene selection methods are efficient, effective, and robust in identifying differentially expressed genes. Adopting the existing SVM-based and KNN-based classifiers, the selected genes by our proposed methods in general give more accurate classification results, typically when the sample class sizes in the training dataset are unbalanced
Randomized algorithms for fully online multiprocessor scheduling with testing
We contribute the first randomized algorithm that is an integration of
arbitrarily many deterministic algorithms for the fully online multiprocessor
scheduling with testing problem. When there are two machines, we show that with
two component algorithms its expected competitive ratio is already strictly
smaller than the best proven deterministic competitive ratio lower bound. Such
algorithmic results are rarely seen in the literature. Multiprocessor
scheduling is one of the first combinatorial optimization problems that have
received numerous studies. Recently, several research groups examined its
testing variant, in which each job arrives with an upper bound on
the processing time and a testing operation of length ; one can choose to
execute for time, or to test for time to obtain the
exact processing time followed by immediately executing the job for
time. Our target problem is the fully online version, in which the jobs arrive
in sequence so that the testing decision needs to be made at the job arrival as
well as the designated machine. We propose an expected -competitive randomized algorithm as a non-uniform
probability distribution over arbitrarily many deterministic algorithms, where
is the Golden ratio. When there are two
machines, we show that our randomized algorithm based on two deterministic
algorithms is already expected -competitive. Besides, we use Yao's principle to prove lower
bounds of and on the expected competitive ratio for any
randomized algorithm at the presence of at least three machines and only two
machines, respectively, and prove a lower bound of on the competitive
ratio for any deterministic algorithm when there are only two machines.Comment: 21 pages with 1 plot; an extended abstract to be submitte
ComPhy: Prokaryotic Composite Distance Phylogenies Inferred from Whole-Genome Gene Sets
doi:10.1186/1471-2105-10-S1-S5With the increasing availability of whole genome sequences, it is becoming more and more important to use complete genome sequences for inferring species phylogenies. We developed a new tool ComPhy, 'Composite Distance Phylogeny', based on a composite distance matrix calculated from the comparison of complete gene sets between genome pairs to produce a prokaryotic phylogeny. The composite distance between two genomes is defined by three components: Gene Dispersion Distance (GDD), Genome Breakpoint Distance (GBD) and Gene Content Distance (GCD). GDD quantifies the dispersion of orthologous genes along the genomic coordinates from one genome to another; GBD measures the shared breakpoints between two genomes; GCD measures the level of shared orthologs between two genomes. The
phylogenetic tree is constructed from the composite distance matrix using a neighbor
joining method. We tested our method on 9 datasets from 398 completely sequenced
prokaryotic genomes. We have achieved above 90% agreement in quartet topologies between the tree created by our method and the tree from the Bergey's taxonomy. In comparison to several other phylogenetic analysis methods, our method showed consistently better performance. ComPhy is a fast and robust tool for genome-wide inference of evolutionary
relationship among genomes."This work was supported in part by NSF/ITR-IIS-0407204.
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