# Linear Assignment Problem

approximate dual projective algorithm by Ramakrishnan et al.) and algorithms that use forest construction as dual forest algorithm by Achatz et al.The auction algorithm is considered one of the fastest algorithm that can find the optimal solution for the assignment problem.DGS was developed to fulfill these requirement and in our context it sacrificed a mere 0.6% of the optimal solution obtained by the auction algorithm while attaining a substantial speedup in terms of computational time.

approximate dual projective algorithm by Ramakrishnan et al.) and algorithms that use forest construction as dual forest algorithm by Achatz et al.The auction algorithm is considered one of the fastest algorithm that can find the optimal solution for the assignment problem.DGS was developed to fulfill these requirement and in our context it sacrificed a mere 0.6% of the optimal solution obtained by the auction algorithm while attaining a substantial speedup in terms of computational time.

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The fact that the auction algorithm only gives a partial assignment if interrupted makes it more unsuitable.

We deduced that the auction algorithm would be impractical for our system and other applications where execution time is strictly constrained and a solution needs to be found before a certain deadline.

Even as the auction is considered one of the fastest algorithms, for large-scale and complex instances of the assignment problem the auction algorithm can take a lot of time to find the optimal solution. discussed five types of the assignment problem instances which are Geometric, Fixed-Cost, High-Cost, Low-Cost and Uniformly Random.

It was shown that for the first two problem types the auction algorithm performs poorly in terms of the running time in comparison with the other three problem types.

This application requires solving instances of the assignment problem with n 10, 000 persons and objects in less than one minute.

This has to be done periodically and in a reasonable time as the peers are watching and transmitting a live stream.I understand that the proposed problem is a relaxed version of the RLAP.But my intuition is that the optimum for the relax problem should occur at "vertex".Authors: Amgad Naiem, Mohammed El-Beltagy INTRODUCTION The linear sum assignment problem (LSAP) is a classical combinatorial optimization problems that is found in many applications.The assignment problem deals with the question of how to assign n persons to n objects in the best possible way.The auction algorithm proved to be unsuitable for our application.Even attempts of a parallelized version of the auction algorithm did not meet our requirements.I.e., the Square Assignment Problem can be solved as a Continuous Linear Program and will produce the correct optimal objective value for the Assignment Problem constrained to have integer (binary) solutions.Therefore, the Rectangular Assignment Problem can also be solved as a Continuous Linear Program and will produce the correct optimal objective value.For instances of the Geometric and Fixed-Cost types with n = 10, 000, the auction algorithm can take hours to finish.The application that motived DGS was the centralized P2P live streaming system discussed in “On the feasibility of centrally-coordinated peer-to-peer live streaming”.

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In the general linear programming model of the assignment problem, one agent is assigned to one and only one task. The assignment problem is a special case of the…

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Techniques, many of which built on linear programming for generating a global view of large, complex optimization problems 5. 2. Mathemtical LP Model for assignment problem Some linear programming models for the assignment problem is presented is assumed that the cost or time for every machine is known denoting that C…

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Assignment Problem Linear Programming The assignment problem is a special type of transportation problem, where the objective is to minimize the cost or time of completing a number of jobs by a number of persons.…

• ###### Scipy.optimize.linear_sum_assignment — SciPy v1.3.0 Reference Guide

The linear sum assignment problem is also known as minimum weight matching in bipartite graphs. A problem instance is described by a matrix C, where each Ci,j is the cost of matching vertex i of the first partite set a “worker” and vertex j of the second set a “job”. The goal is to find a complete assignment of workers to jobs of minimal cost.…

• ###### LAPJV - Jonker-Volgenant Algorithm for Linear Assignment Problem V3.0.

The Jonker-Volgenant algorithm is much faster than the famous Hungarian algorithm for the Linear Assignment Problem LAP. This Matlab implementation is modified from the original C++ code made by Roy Jonker, one of the inventors of the algorithm. It is about 10 times faster than the munkres code v2.2 of the author.…