Two commodity network flows and linear programming

1973 ◽  
Vol 4 (1) ◽  
pp. 1-20 ◽  
Author(s):  
M. Sakarovitch
Keyword(s):  
Linear Programming ◽  
Network Flows

Overlay Multicast Optimization: IBM ILOG CPLEX

2012 ◽  
Vol 58 (4) ◽  
pp. 381-388 ◽  
Author(s):  
Michał Kucharzak ◽  
Dawid Zydek ◽  
Iwona Poźniak-Koszałka
Keyword(s):  
Linear Programming ◽  
Network Flows ◽  
Academic Research ◽  
Mixed Integer ◽  
Overlay Multicast ◽  
Complex Optimization ◽  
Linear Problems ◽  
Global Parameters

Abstract IBM ILOG CPLEX Optimization Studio delivers advanced and complex optimization libraries that solve linear programming (LP) and related problems, e.g., mixed integer. Moreover, the optimization tool provides users with its Academic Research Edition, which is available for teaching and noncommercial research at no-charge. This paper describes the usage of CPLEX C++ API for solving linear problems and, as an exhaustive example, optimization of network flows in overlay multicast is taken into account. Applying continuous and integral variables and implementing various constraints, including equations and inequalities, as well as setting some global parameters of the solver are presented and widely explained.

Linear Programming and Network Flows

1978 ◽  
Vol 29 (5) ◽  
pp. 510
Author(s):  
C. R. Sergeant ◽  
Mokhtar S. Bazaraa ◽  
John J. Jarvis
Keyword(s):  
Linear Programming ◽  
Network Flows

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.

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