Donglei Du

Preemptive on-line scheduling for two uniform processors

This paper considers the problem of preemptive on-line scheduling for two uniform processors in which one of the processors has speed 1 and the other has speed s>=1. The objective is to minimize the makespan. A best possible algorithm with competitive ratio of (1+s)^2/(1+s+s^2) is proposed for this problem.

The k-level facility location game

We propose a cost-sharing scheme for the k-level facility location game that is cross-monotonic, competitive, and 6-approximate cost recovery. This extends the recent result for the 1-level facility location game of Pal and Tardos.

Variation, Evolution, and Correlation Analysis of C+G Content and Genome or Chromosome Size in Different Kingdoms and Phyla

C+G content (GC content or G+C content) is known to be correlated with genome/chromosome size in bacteria but the relationship for other kingdoms remains unclear. This study analyzed genome size, chromosome size, and base composition in most of the available sequenced genomes in various kingdoms. Genome size tends to increase during evolution in plants and animals, and the same is likely true for bacteria. The genomic C+G contents were found to vary greatly in microorganisms but were quite similar within each animal or plant subkingdom. In animals and plants, the C+G contents are ranked as follows: monocot plants>mammals>non-mammalian animals>dicot plants. The variation in C+G content between chromosomes within species is greater in animals than in plants. The correlation between average chromosome C+G content and chromosome length was found to be positive in Proteobacteria, Actinobacteria (but not in other analyzed bacterial phyla), Ascomycota fungi, and likely also in some plants; negative in some animals, insignificant in two protist phyla, and likely very weak in Archaea. Clearly, correlations between C+G content and chromosome size can be positive, negative, or not significant depending on the kingdoms/groups or species. Different phyla or species exhibit different patterns of correlation between chromosome-size and C+G content. Most chromosomes within a species have a similar pattern of variation in C+G content but outliers are common. The data presented in this study suggest that the C+G content is under genetic control by both trans- and cis- factors and that the correlation between C+G content and chromosome length can be positive, negative, or not significant in different phyla.

Improved Approximation Algorithms for the Facility Location Problems with Linear/Submodular Penalties

We consider the facility location problem with submodular penalties (FLPSP) and the facility location problem with linear penalties (FLPLP), two extensions of the classical facility location problem (FLP). First, we introduce a general algorithmic framework for a class of covering problems with submodular penalties, extending the recent result of Geunes et al. (Math Program 130:85–106, 2011) with linear penalties. This framework leverages existing approximation results for the original covering problems to obtain corresponding results for their counterparts with submodular penalties. Specifically, any LP-based

Improved Approximation Algorithms for the Facility Location Problems with Linear/submodular Penalty

\alpha

Optimal preemptive semi-online scheduling on two uniform processors

α-approximation for the original covering problem can be leveraged to obtain an

An approximation algorithm for the k-level stochastic facility location problem

\left( 1-e^{-1/\alpha }\right) ^{-1}