scholarly journals Bounds for the Lonely Runner Problems Via Linear Programming

2021 ◽  
Author(s):  
Felipe Gonçalves ◽  
João P. G. Ramos
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Programming Framework

AbstractIn this note we develop a linear programming framework to produce upper and lower bounds for the lonely runner problem.

Linear programming computation of upper and lower bounds of viscoelastic functions

1972 ◽  
Vol 6 (3) ◽  
pp. 479-482 ◽  
Author(s):  
Donald A. Mcquarrie ◽  
Ronald T. Jamieson ◽  
Mitchel Shen
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Upper And Lower Bounds

scholarly journals Bound Propagation

2003 ◽  
Vol 19 ◽  
pp. 139-154 ◽  
Author(s):  
M. Leisink ◽  
B. Kappen
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Graphical Model ◽  
Probability Distributions ◽  
Directed Graphs ◽  
Upper And Lower Bounds ◽  
Marginal Probability ◽  
Practical Applications ◽  
Marginal Values ◽  
Small Clusters

In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The range of allowed probability distributions over the surrounding nodes is restricted using earlier computed bounds. As we will show, this can be considered as a set of constraints in a linear programming problem of which the objective function is the marginal probability of the center nodes. In this way knowledge about the maginals of neighbouring clusters is passed to other clusters thereby tightening the bounds on their marginals. We show that sharp bounds can be obtained for undirected and directed graphs that are used for practical applications, but for which exact computations are infeasible.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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