From linear programming to graph theory: Standardization of the algebraic model of timed event graphs

2009 ◽  
Author(s):  
Abdelhak Guezzi ◽  
Philippe Declerck
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
Algebraic Model ◽  
Timed Event Graphs

Multivariate product-type lower bounds

2001 ◽  
Vol 38 (02) ◽  
pp. 407-420
Author(s):  
Henry W. Block ◽  
Tuhao Chen
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
Lower Bounds ◽  
Product Type ◽  
Probability Inequalities ◽  
Programming Techniques

Univariate probability inequalities have received extensive attention. It has been shown that under certain conditions, product-type bounds are valid and sharper than summation-type bounds. Although results concerning multivariate inequalities have appeared in the literature, product-type bounds in a multivariate setting have not yet been studied. This note explores an approach using graph theory and linear programming techniques to construct product-type lower bounds for the probability of the intersection among unions of k sets of events.

Block Design Games

1961 ◽  
Vol 13 ◽  
pp. 110-128 ◽  
Author(s):  
A. J. Hoffman ◽  
Moses Richardson
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
Network Flows ◽  
Automorphism Groups ◽  
Block Design ◽  
The Other ◽  
Block Designs ◽  
Simple Games ◽  
Extensive Family ◽  
Natural Way

In this paper, we define and begin the study of an extensive family of simple n-person games based in a natural way on block designs, and hitherto for the most part unexplored except for the finite projective games (13). They should serve at least as a proving ground for conjectures about simple games. It is shown that many of these games are not strong and that many do not possess main simple solutions. In other cases, it is shown that they have no equitable main simple solution, that is, one in which the main simple vector has equal components. On the other hand, the even-dimensional finite projective games PG(2s, pn) with s > 1 possess equitable main simple solutions, although they are not strong either. These results are obtained by means of the study of the possible blocking coalitions. Interpretations in terms of graph theory, network flows, and linear programming are discusssed, as well as k-stability, automorphism groups, and some unsolved problems.

scholarly journals On Computation of Recently Defined Degree-Based Topological Indices of Some Families of Convex Polytopes via M-Polynomial

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Deeba Afzal ◽  
Farkhanda Afzal ◽  
Mohammad Reza Farahani ◽  
Samia Ali
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
Significant Role ◽  
Convex Polytopes ◽  
Topological Indices ◽  
Connectivity Index ◽  
Atom Bond

Topological indices are of incredible significance in the field of graph theory. Convex polytopes play a significant role both in various branches of mathematics and also in applied areas, most notably in linear programming. We have calculated some topological indices such as atom-bond connectivity index, geometric arithmetic index, K-Banhatti indices, and K-hyper-Banhatti indices and modified K-Banhatti indices from some families of convex polytopes through M-polynomials. The M-polynomials of the graphs provide us with a great help to calculate the topological indices of different structures.

Multivariate product-type lower bounds

2001 ◽  
Vol 38 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Henry W. Block ◽  
Tuhao Chen
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
Lower Bounds ◽  
Product Type ◽  
Probability Inequalities ◽  
Programming Techniques

Univariate probability inequalities have received extensive attention. It has been shown that under certain conditions, product-type bounds are valid and sharper than summation-type bounds. Although results concerning multivariate inequalities have appeared in the literature, product-type bounds in a multivariate setting have not yet been studied. This note explores an approach using graph theory and linear programming techniques to construct product-type lower bounds for the probability of the intersection among unions of k sets of events.

Random Factors in the Construction Organization

2012 ◽  
Vol 174-177 ◽  
pp. 3268-3273
Author(s):  
Zhong Yi ◽  
Cheng Zhi Yuan
Keyword(s):  
Linear Programming ◽  
Graph Theory ◽  
National Economy ◽  
Mathematical Description ◽  
Critical Path ◽  
Planning Method ◽  
Engineering Analysis ◽  
Analysis Method ◽  
Critical Path Method ◽  
Construction Organization

The construction organization usually takes the Critical Path Method (CPM ) used in the mathematics graph theory, which is a kind of classic system engineering analysis method, was introduced to China by Hua Luogeng – a mathematician, and originally called the Overall Planning Method. This method has been widely applied in various fields of the national economy, especially in the construction field; of course the Overall Planning Method itself has also been greatly developed. Though the Overall Planning Method is relatively mature, there are still a number of uncertainties (random factors) in the construction organization, and it is not easy to make a mathematical description for the Critical Path Method. This paper tries to use random linear programming in the construction organization.

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