A MapReduce Algorithm for Minimum Vertex Cover Problems and Its Randomization

MapReduce is a programming paradigm for large-scale distributed information processing. This paper proposes a MapReduce algorithm for the minimum vertex cover problem, which is known to be NP-hard. The MapReduce algorithm can efficiently obtain a minimal vertex cover in a small number of rounds. We show the effectiveness of the algorithm, through experimental evaluation and comparison with exact and approximate algorithms that it demonstrates high quality in a small number of MapReduce rounds. We also confirm from experimentation that the algorithm has good scalability, allowing high-quality solutions under restricted computation times due to increased graph size. Moreover, we extend our algorithm to randomized one to obtain good expected approximate ratio

Petri Net Modeling for Ising Model Formulation in Quantum Annealing

Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation

Search for Human-Specific Proteins Based on Availability Scores of Short Constituent Sequences: Identification of a WRWSH Protein in Human Testis

Little is known about protein sequences unique in humans. Here, we performed alignment-free sequence comparisons based on the availability (frequency bias) of short constituent amino acid (aa) sequences (SCSs) in proteins to search for human-specific proteins. Focusing on 5-aa SCSs (pentats), exhaustive comparisons of availability scores among the human proteome and other nine mammalian proteomes in the nonredundant (nr) database identified a candidate protein containing WRWSH, here called FAM75, as human-specific. Examination of various human genome sequences revealed that FAM75 had genomic DNA sequences for either WRWSH or WRWSR due to a single nucleotide polymorphism (SNP). FAM75 and its related protein FAM205A were found to be produced through alternative splicing. The FAM75 transcript was found only in humans, but the FAM205A transcript was also present in other mammals. In humans, both FAM75 and FAM205A were expressed specifically in testis at the mRNA level, and they were immunohistochemically located in cells in seminiferous ducts and in acrosomes in spermatids at the protein level, suggesting their possible function in sperm development and fertilization. This study highlights a practical application of SCS-based methods for protein searches and suggests possible contributions of SNP variants and alternative splicing of FAM75 to human evolution

A Petri Net Approach to Generate Integer Linear Programming Problems

This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem

Rule-based Assembly for Short-read Datasets Obtained with Multiple Assemblers and k-mer Sizes

Various de novo assembly methods based on the concept of k-mer have been proposed. Despite the success of these methods, an alternative approach, referred to as the hybrid approach, has recently been proposed that combines different traditional methods to effectively exploit each of their properties in an integrated manner. However, the results obtained from the traditional methods used in the hybrid approach depend not only on the specific algorithm or heuristics but also on the selection of a user-specific k-mer size. Consequently, the results obtained with the hybrid approach also depend on these factors. Here, we designed a new assembly approach, referred to as the rule-based assembly. This approach follows a similar strategy to the hybrid approach, but employs specific rules learned from certain characteristics of draft contigs to remove any erroneous contigs and then merges them. To construct the most effective rules for this purpose, a learning method based on decision trees, i.e., a complex decision tree, is proposed. Comparative experiments were also conducted to validate the method. The results showed that proposed method could outperformed traditional methods in certain cases

Resource assignment and scheduling based on a two-phase metaheuristic for cropping system

This paper proposes a resource assignment and scheduling based on a two-phase metaheuristic for a long-term cropping schedule. The two-phase metaheuristic performs the optimization of resources assignment and scheduling based on a simulated annealing (SA), a genetic algorithm (GA) and a hybrid Petri nets model. The initial and progressive states of farmlands and resources, moving sequence of machinery, cooperative work, and deadlock removal have been well handled in the proposed approach. In the computational experiment, the schemes of emphasizing the resource assignment optimization, initializing the population of the GA with chromosomes sorted by the waiting time, and inheriting the priority list from tasks in the previous resources assignment improved the evolution speed and solution quality. The simulated result indicated that the formulated schedule has a high ratio of resource utilization in sugarcane production. The proposed approach also contributes a referential scheme for applying the metaheuristic approach to other crop production scheduling

Hybrid Petri nets modeling for farm work flow

This paper introduces hybrid Petri nets into modeling for farm work flow in agricultural production. The main emphasis is on the construction of an adequate model for designing practical farm work planning for agriculture production corporations. Hybrid Petri nets conventionally comprise a continuous part and a discrete part. The continuous part mainly models the practical work in the farmland, and the discrete part mainly represents the status changes in resources such as machinery and labor. The proposed model also models the present status or undesirable breaks during the farming process. Moreover, in this paper, the approach of formulating the farm work planning problem based on the model is suggested. The simulated results reveal that the hybrid Petri nets model is promising for exactly describing the farming process and reallocating resources in the presence of uncertainties. The proposed model serves as a referential model for farm work planning and it promotes the development of a corresponding optimization algorithm under uncertain environments

A frequency-based linguistic approach to protein decoding and design: Simple concepts, diverse applications, and the SCS Package

Protein structure and function information is coded in amino acid sequences. However, the relationship between primary sequences and three-dimensional structures and functions remains enigmatic. Our approach to this fundamental biochemistry problem is based on the frequencies of short constituent sequences (SCSs) or words. A protein amino acid sequence is considered analogous to an English sentence, where SCSs are equivalent to words. Availability scores, which are defined as real SCS frequencies in the non-redundant amino acid database relative to their probabilistically expected frequencies, demonstrate the biological usage bias of SCSs. As a result, this frequency-based linguistic approach is expected to have diverse applications, such as secondary structure specifications by structure-specific SCSs and immunological adjuvants with rare or non-existent SCSs. Linguistic similarities (e.g., wide ranges of scale-free distributions) and dissimilarities (e.g., behaviors of low-rank samples) between proteins and the natural English language have been revealed in the rank-frequency relationships of SCSs or words. We have developed a web server, the SCS Package, which contains five applications for analyzing protein sequences based on the linguistic concept. These tools have the potential to assist researchers in deciphering structurally and functionally important protein sites, species-specific sequences, and functional relationships between SCSs. The SCS Package also provides researchers with a tool to construct amino acid sequences de novo based on the idiomatic usage of SCSs