Algorithm 1015

2021 ◽  
Vol 47 (2) ◽  
pp. 1-27
Author(s):  
Stefan Guthe ◽  
Daniel Thuerck
Keyword(s):  
Shortest Path ◽  
Assignment Problem ◽  
Parallel Implementation ◽  
Shortest Path Algorithm ◽  
Cost Matrix ◽  
The Past ◽  
Path Search ◽  
Dual Variables ◽  
The Cost ◽  
Real World Problems

We present a new algorithm for solving the dense linear (sum) assignment problem and an efficient, parallel implementation that is based on the successive shortest path algorithm. More specifically, we introduce the well-known epsilon scaling approach used in the Auction algorithm to approximate the dual variables of the successive shortest path algorithm prior to solving the assignment problem to limit the complexity of the path search. This improves the runtime by several orders of magnitude for hard-to-solve real-world problems, making the runtime virtually independent of how hard the assignment is to find. In addition, our approach allows for using accelerators and/or external compute resources to calculate individual rows of the cost matrix. This enables us to solve problems that are larger than what has been reported in the past, including the ability to efficiently solve problems whose cost matrix exceeds the available systems memory. To our knowledge, this is the first implementation that is able to solve problems with more than one trillion arcs in less than 100 hours on a single machine.

Searching Best Strategies Algorithm for the No Balance Assignment Problem

2011 ◽  
Vol 50-51 ◽  
pp. 386-390
Author(s):  
Mao Yan Fang ◽  
Min Le Wang ◽  
Yi Ming Bi
Keyword(s):  
Assignment Problem ◽  
Cost Matrix ◽  
Classical Algorithm ◽  
The Cost

The No Balance Assignment Problem (NBAP) is mainly resolved by changing it into Balance Assignment Problem (BAP) and using classical algorithm to deal with it now. This paper proposed Searching Best strategies Algorithm (SBSA) to resolve this problem, and it needn’t to change NBAP into BAP. SBSA resolves NBAP based on searching the best answer of the cost matrix. This algorithm’s theory is simple，and it is easy to operate. The result of the research indicate that the algorithm not only can deal with NBAP, but also can deal with BAP and other problems such as translation problem.

Parallel Implementation of the Shortest Path Algorithm on FPGA

2008 ◽  
Author(s):  
Ivan Fernandez ◽  
Javier Castillo ◽  
Cesar Pedraza ◽  
Carlos Sanchez ◽  
Jose Ignacio Martinez
Keyword(s):  
Shortest Path ◽  
Parallel Implementation ◽  
Shortest Path Algorithm

Accelerating Traffic Assignment with Customizable Contraction Hierarchies

2020 ◽  
Vol 2674 (1) ◽  
pp. 188-196 ◽  
Author(s):  
Arne Schneck ◽  
Klaus Nökel
Keyword(s):  
Shortest Path ◽  
Traffic Assignment ◽  
Shortest Path Problem ◽  
Transport Modeling ◽  
The Past ◽  
Acceleration Techniques ◽  
Network Loading ◽  
Enormous Amount ◽  
Path Search ◽  
Shortest Path Search

In many algorithms for traffic assignment, the most time-consuming step is shortest path search between all O–D pairs. Almost unnoticed by the transport modeling community, there has been an enormous amount of research on acceleration techniques for the shortest path problem in road networks in the past decade. These techniques usually divide the problem into a relatively expensive preprocessing phase and a significantly accelerated search phase. In this paper, the recently developed customizable contraction hierarchies are used for both shortest path search and network loading in the bi-conjugate Frank–Wolfe algorithm. For the largest test network, this approach achieves a speedup by a factor of 42 compared with a straightforward implementation of Dijkstra’s algorithm.

Parallel Implementation of Single-Source Shortest Path Algorithm Based on Haloop

2012 ◽  
Vol 220-223 ◽  
pp. 2428-2432 ◽  
Author(s):  
Yuan Sheng Lou ◽  
Wen Yuan Zhang ◽  
Feng Xu ◽  
Yu Wang ◽  
Sheng Chen
Keyword(s):  
Shortest Path ◽  
Parallel Implementation ◽  
Program Execution ◽  
Single Source ◽  
Shortest Path Algorithm ◽  
Typical Problem ◽  
Mapreduce Framework ◽  
Programming Framework ◽  
Wide Range ◽  
Hadoop Framework

As a typical problem of graph theory, Single-Source Shortest Path(SSSP) has a wide range of applications and research. The traditional MapReduce framework such as Hadoop has been applied to SSSP problem. However, in this way, it may need writing and reading the disk frequently, transmitting data largely, beacuse of SSSP’s iterative. Haloop is a parallel programming framework which makes an improvement based on Hadoop framework, and adapts itself to iterative programming. Hence, this article represents the SSSP problem with an iterative way firstly, and then we put forward the implementation mechanism of SSSP algorithm based on Haloop. Though testing and analyzing, the implementation based on Haloop obviously improves the efficiency of program execution, compared with the traditional realization mechanism.

scholarly journals Identification of Novel Thyroid Cancer-Related Genes and Chemicals Using Shortest Path Algorithm

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Jiang ◽  
Peiwei Zhang ◽  
Li-Peng Li ◽  
Yi-Chun He ◽  
Ru-jian Gao ◽  
...  
Keyword(s):  
Thyroid Cancer ◽  
Shortest Path ◽  
Disease Genes ◽  
Shortest Path Algorithm ◽  
The Past ◽  
Disease Identification ◽  
Effective Treatments

Thyroid cancer is a typical endocrine malignancy. In the past three decades, the continued growth of its incidence has made it urgent to design effective treatments to treat this disease. To this end, it is necessary to uncover the mechanism underlying this disease. Identification of thyroid cancer-related genes and chemicals is helpful to understand the mechanism of thyroid cancer. In this study, we generalized some previous methods to discover both disease genes and chemicals. The method was based on shortest path algorithm and applied to discover novel thyroid cancer-related genes and chemicals. The analysis of the final obtained genes and chemicals suggests that some of them are crucial to the formation and development of thyroid cancer. It is indicated that the proposed method is effective for the discovery of novel disease genes and chemicals.

scholarly journals A Review: Parallel Implementation of Shortest path Algorithm on GPGPU

IJARCCE ◽  
2017 ◽  
Vol 6 (5) ◽  
pp. 345-348
Author(s):  
Avadhoot K. Katkar ◽  
Dr. Kulkarni D. B.
Keyword(s):  
Shortest Path ◽  
Parallel Implementation ◽  
Shortest Path Algorithm

Measuring the cost of environmental compliance for Waikato dairy farmers - a survey approach

2015 ◽  
Vol 77 ◽  
pp. 159-166
Author(s):  
T.O.R. Macdonald ◽  
J.S. Rowarth ◽  
F.G. Scrimgeour
Keyword(s):  
Qualitative Data ◽  
Management Practice ◽  
Dairy Farm ◽  
Environmental Compliance ◽  
Dairy Farmers ◽  
The Past ◽  
Farm Systems ◽  
The Cost ◽  
Farm System ◽  
Survey Approach

The link between dairy farm systems and cost of environmental compliance is not always clear. A survey of Waikato dairy farmers was conducted to establish the real (non-modelled) cost of compliance with environmental regulation in the region. Quantitative and qualitative data were gathered to improve understanding of compliance costs and implementation issues for a range of Waikato farm systems. The average oneoff capital cost of compliance determined through a survey approach was $1.02 per kg milksolids, $1490 per hectare and $403 per cow. Costs experienced by Waikato farmers have exceeded average economic farm surplus for the region in the past 5 years. As regulation increases there are efficiencies to be gained through implementing farm infrastructure and farm management practice to best match farm system intensity. Keywords: Dairy, compliance, farm systems, nitrogen, Waikato

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

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