MULTI-SOURCE SPANNING TREE PROBLEMS

2000 ◽  
Vol 01 (01) ◽  
pp. 61-71 ◽  
Author(s):  
ARTHUR M. FARLEY ◽  
PARASKEVI FRAGOPOULOU ◽  
DAVID KRUMME ◽  
ANDRZEJ PROSKUROWSKI ◽  
DANA RICHARDS
Keyword(s):  
Exact Solution ◽  
Spanning Tree ◽  
Polynomial Solution ◽  
Solution Algorithm ◽  
Efficient Algorithms ◽  
Strong Sense ◽  
Alternative Measure ◽  
Multicast Communication ◽  
Multiple Sources ◽  
Sum Of Distances

We consider a model of multicast communication in a network whereby multiple sources have messages to disseminate among all sites of a network. We propose that the messages from all sources are disseminated along the same spanning tree of the network and consider the problem of constructing an optimal such tree. One measure for suitability of the construction is the sum of distances from all sources to all other vertices. We show that finding the exact solution in this case in [Formula: see text]-hard (in the strong sense). We then investigate solutions for some restricted classes of graphs and give efficient algorithms for those. We also consider an alternative measure of goodness for the spanning tree, being the maximum eccentricity of a source. We show that the problem of finding such a minimum eccentricity spanning tree is somewhat easier to solve and give a pseudo-polynomial solution algorithm.

Exact solution approaches for the Multi-period Degree Constrained Minimum Spanning Tree Problem

2018 ◽  
Vol 271 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Rosklin Juliano Chagas ◽  
Cristiano Arbex Valle ◽  
Alexandre Salles da Cunha
Keyword(s):  
Exact Solution ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Minimum Spanning Tree Problem

A Logit Model for Budget Allocation Subject to Multi Budget Sources

2011 ◽  
Vol 2 (3) ◽  
pp. 1-17 ◽  
Author(s):  
Saeed A. Bagloee ◽  
Christopher G. Reddick
Keyword(s):  
Logit Model ◽  
Large Scale ◽  
Budget Allocation ◽  
Solution Algorithm ◽  
Influential Factors ◽  
Programming Formulation ◽  
Extended System ◽  
Multiple Sources ◽  
Unknown Parameters ◽  
Allocation Process

In a complex and extended system such as a government, the proper allocation of the budget to its sub-entities is always a major challenge. As such for cases like governments, a situation in which multiple budget sources with different concerns available to the sub-entities is common. This study develops an applicable model for large-scale cases in which identifying the flow of capital or budget from (multiple) sources to the sub-entities is sought. Since the influential factors to the allocation process may be mingled with some unknown parameters (as well as known factors) a logit model is developed from past panel data. The logit model is based on the concept of utility, which quantifies the advantage of approaching budget-sources for the sub-entities. Then the budget allocation problem of logit form is written as a mathematical programming formulation for which Successive Coordinate Descent (SCD) method is proposed as the solution algorithm. In this paper, the proposed methodology is tested numerically. The results of this study show there is strong evidence that some of the entities’ properties can be altered in order to achieve a better budget allocation.

scholarly journals EFFICIENT ALGORITHMS FOR TRAVELLING SALESMAN PROBLEMS ARISING IN WAREHOUSE ORDER PICKING

2015 ◽  
Vol 57 (2) ◽  
pp. 166-174 ◽  
Author(s):  
H. CHARKHGARD ◽  
M. SAVELSBERGH
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Linear Time ◽  
Optimal Solution ◽  
Efficient Algorithms ◽  
Order Picking ◽  
Travelling Salesman ◽  
Routing Problems ◽  
Parallel Lines

We investigate two routing problems that arise when order pickers traverse an aisle in a warehouse. The routing problems can be viewed as Euclidean travelling salesman problems with points on two parallel lines. We show that if the order picker traverses only a section of the aisle and then returns, then an optimal solution can be found in linear time, and if the order picker traverses the entire aisle, then an optimal solution can be found in quadratic time. Moreover, we show how to approximate the routing cost in linear time by computing a minimum spanning tree for the points on the parallel lines.

Vehicle Sequencing at Transshipment Terminals with Handover Relations

2020 ◽  
Author(s):  
Dirk Briskorn ◽  
Malte Fliedner ◽  
Martin Tschöke
Keyword(s):  
Exact Solution ◽  
Computational Study ◽  
Solution Algorithm ◽  
Comprehensive Analysis ◽  
Container Terminals ◽  
Decision Problems ◽  
Operational Planning ◽  
Vast Number ◽  
Synchronization Problem ◽  
Structural Connections

Operational planning at transshipment nodes is a wide and challenging field of research that covers a vast number of distinct relevant applications, spanning from seaport container terminals to rail terminals to cross-docks. In this work, we study the feasibility version of a fundamental synchronization problem that assigns incoming vehicles to docking resources subject to handover relations. We carry out a comprehensive analysis of computational complexity of various problem variants and establish structural connections to famous decision problems in graph theory. We further propose an exact solution algorithm for finding feasible dock assignments, if vehicles can visit the node only once and evaluate its performance in a comprehensive computational study.

scholarly journals Numerical Approximation of Fredholm Integral Equation (FIE) of 2nd Kind using Galerkin and Collocation Methods

2019 ◽  
Vol 38 ◽  
pp. 11-25
Author(s):  
Hasib Uddin Molla ◽  
Goutam Saha
Keyword(s):  
Exact Solution ◽  
Galerkin Method ◽  
Collocation Method ◽  
Exact Analytical Solution ◽  
Polynomial Solution ◽  
Hermite Polynomials ◽  
Research Work ◽  
Basis Functions ◽  
Collocation Methods ◽  
Galerkin And Collocation Methods

In this research work, Galerkin and collocation methods have been introduced for approximating the solution of FIE of 2nd kind using LH (product of Laguerre and Hermite) polynomials which are considered as basis functions. Also, a comparison has been done between the solutions of Galerkin and collocation method with the exact solution. Both of these methods show the outcome in terms of the approximate polynomial which is a linear combination of basis functions. Results reveal that performance of collocation method is better than Galerkin method. Moreover, five different polynomials such as Legendre, Laguerre, Hermite, Chebyshev 1st kind and Bernstein are also considered as a basis functions. And it is found that all these approximate solutions converge to same polynomial solution and then a comparison has been made with the exact solution. In addition, five different set of collocation points are also being considered and then the approximate results are compared with the exact analytical solution. It is observed that collocation method performed well compared to Galerkin method. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 11-25

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