Un algoritmo para el problema de biflujo máximo simétrico no dirigido

En este trabajo proponemos un algoritmo de O(nmlogU) para resolver el problema de biflujo máximo simétrico en una red no dirigida. Para resolver este problema se introduce un cambio de variable que permite dividir el problema original en dos problemas de flujo máximo. De esta manera se obtiene un algoritmo sencillo y eficiente donde se utilizan las herramientas computacionales propias de la resolución del clásico problema de maximizar un único flujo

A software application to optimize the visits of sales/marketing agents to their customers in a brewing company

We present a software application developed to optimize the annual planning of visits of a brewing company’s sales/marketing staff to their customers. Each of these customers must be annually visited a provided number of times. Thus, each salesperson is assigned to a set of customers that must be visited each week. The application will assign all the visits of a salesperson to each customer so that all weeks should have more or less the same number of visits. By virtue of this approach, the brewing company diminished their marketing operating costs, as well as improved their customer relationships

Una variante del algoritmo de Ahuja-Orlin para problemas de flujo máximo: experiencias computacionales y comparaciones

En este trabajo se introduce una variante del algoritmo de escalado de Ahuja y Orlin, con la misma complejidad computacional teórica, para resolver problemas de flujo máximo en redes sin circuitos. Como se constata en las experiencias computacionales que hemos realizado sobre problemas generados aleatoriamente, en el noventa por ciento de los casos el tiempo de CPU del nuevo procedimiento es significativamente inferior

On the K shortest path trees problem

We address the problem of finding the K best path trees connecting a source node with any other non-source node in a directed network with arbitrary lengths. The main result in this paper is the proof that the kth shortest path tree is adjacent to at least one of the previous (k-1) shortest path trees. Consequently, we design an O(f(n,m,Cmax)+Km) time and O(K+m) space algorithm to determine the K shortest path trees, in a directed network with n nodes, m arcs and maximum absolute length Cmax, where O(f(n,m,Cmax)) is the best time needed to solve the shortest simple paths connecting a source node with any other non-source node.Network/graphs K shortest path trees problem Shortest path tree problem K best spanning tree K best solutions

SHORTEST PATH SIMPLEX ALGORITHM WITH A MULTIPLE PIVOT RULE: A COMPARATIVE STUDY

This paper introduces a new multiple pivot shortest path simplex method by choosing a subset of non-basic arcs to simultaneously enter into the basis. It is shown that the proposed shortest path simplex method requires O(n) multiple pivots and its running time is O(nm). Results from a computational study comparing the proposed method from previously known methods are reported. The experimental show that the proposed rule is more efficient than the considered shortest path simplex pivot rules.Shortest path problem, simplex shortest path algorithms, multiple pivot rule, experimental analysis

New Dynamic Programming Algorithm for the Multiobjective Minimum Spanning Tree Problem

The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the Minimum Spanning Tree problem, in which the costs associated with every edge of the input graph are vectors. In this paper, we design a new dynamic programming MO-MST algorithm. Dynamic programming for a MO-MST instance leads to the definition of an instance of the One-to-One Multiobjective Shortest Path (MOSP) problem and both instances have equivalent solution sets. The arising MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.Comment: 35 pages; 30 pages without appendix. 4 Tables, 13 Figure