## A PARAMETRIC VISUALIZATION SOFTWARE FOR THE ASSIGNMENT PROBLEM (2005)

### BibTeX

@MISC{Papamanthou05aparametric,

author = {Charalampos Papamanthou and Konstantinos Paparrizos and Nikolaos Samaras},

title = { A PARAMETRIC VISUALIZATION SOFTWARE FOR THE ASSIGNMENT PROBLEM},

year = {2005}

}

### OpenURL

### Abstract

In this paper we present a parametric visualization software used to assist the teaching of the Network Primal Simplex Algorithm for the assignment problem (AP). The assignment problem is a special case of the balanced transportation problem. The main function of the algorithm and design techniques is also presented. Through this process, we aim to underlie the importance and necessity of using such educational methods in order to improve the teaching of Computer Algorithms.

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Citation Context ...r algorithms as well. The techniques used are exactly the same with the techniques used for the NPSA. So, the software has been expanded to solve the AP using the algorithms described in [1], [2] and =-=[7]-=-. Additionally, the software can use the algorithm described in [21] applied in the AP. Moreover, the software has been expanded in order to solve the transportation problem as well, using the algorit... |

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Citation Context ...se new methods of visualization that, according their opinion, could lead to a better presentation of the156 C. Papamanthou, K. Paparrizos, N. Samaras / A Parametric Visualization Software algorithm =-=[27]-=-. All the java applets are available at: http://eos.uom.gr/~samaras/gr/ yujor/yujor.htm. Finally, we must say that Computer Algorithms courses should be escorted by visualization methods so that stude... |

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Citation Context ...esentation will be achieved through a parametric visualization method, which can serve educational purposes and help the instructor explain the algorithm to his audience in a more efficient way [22], =-=[26]-=-. Using our software a user can solve any AP of size less or equal to twenty, unlike most other visualization software that solve a specific example by projecting sequential frames. Additionally, we h... |

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Citation Context ... the techniques used for the NPSA. So, the software has been expanded to solve the AP using the algorithms described in [1], [2] and [7]. Additionally, the software can use the algorithm described in =-=[21]-=- applied in the AP. Moreover, the software has been expanded in order to solve the transportation problem as well, using the algorithms described above. Below, we present some indicative frames produc... |

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Citation Context ...ation problem. It is one of the most classic in the field of Computer Science and Operations Research. A lot of efficient algorithms have been and are constantly being developed for its solution [1], =-=[2]-=-, [3], [4], [6], [9], [10], [11], [16], [19], [20] and [23]. The problem owes its name to the classic application of assigning a number of jobs to an equal number of persons at a minimal total cost, g... |

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Citation Context ...of the visualization of the NPSA we will refer to the algorithm itself and show how it can be applied with the use of pencil and paper. The AP is a special case of the balanced transportation problem =-=[25]-=-. In the AP we just set m = n and ai = bi = 1, i = 1, …, n. So, we say that we have to solve an AP of size n. The mathematical formulation of the AP with a nxn cost matrix is the following: n n min∑∑ ... |

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Citation Context ... kind of resource (i.e. memory). Furthermore, applications of the AP can be found in computer networks design where we are looking for an optimal way to match network nodes with network concentrators =-=[14]-=-. The main purpose of this paper is to present the most often used algorithm; the Network Primal Simplex Algorithm (NPSA). This algorithm was invented in 1947 by G. B. Dantzig [15] and is the most wid... |

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Citation Context ...The presentation will be achieved through a parametric visualization method, which can serve educational purposes and help the instructor explain the algorithm to his audience in a more efficient way =-=[22]-=-, [26]. Using our software a user can solve any AP of size less or equal to twenty, unlike most other visualization software that solve a specific example by projecting sequential frames. Additionally... |

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Citation Context ...oftware will definitely be of great help when the user applies the algorithm himself [26]. Therefore, a computer program has been developed in Java, an object-oriented high level programming language =-=[28]-=-. We chose Java, not only for its object-orientedC. Papamanthou, K. Paparrizos, N. Samaras / A Parametric Visualization Software 151 nature but also for the fact that it is a web-oriented language. J... |