scholarly journals Maximizing the expected number of components in an online search of a graph

2022 ◽  
Vol 345 (1) ◽  
pp. 112668
Author(s):  
Fabrício Siqueira Benevides ◽  
Małgorzata Sulkowska
Keyword(s):  
Online Search ◽  
Expected Number ◽  
Number Of Components

DIAMONDS ARE NOT A MINIMUM WEIGHT TRIANGULATION'S BEST FRIEND

2002 ◽  
Vol 12 (06) ◽  
pp. 445-453 ◽  
Author(s):  
PROSENJIT BOSE ◽  
LUC DEVROYE ◽  
WILLIAM EVANS
Keyword(s):  
Polynomial Time ◽  
Minimum Weight ◽  
Connected Subgraph ◽  
Constant Number ◽  
Point Sets ◽  
Expected Number ◽  
Number Of Components ◽  
Best Friend ◽  
Point Set ◽  
Minimum Weight Triangulation

Two recent methods have increased hopes of finding a polynomial time solution to the problem of computing the minimum weight triangulation of a set S of n points in the plane. Both involve computing what was believed to be a connected or nearly connected subgraph of the minimum weight triangulation, and then completing the triangulation optimally. The first method uses the light graph of S as its initial subgraph. The second method uses the LMT-skeleton of S. Both methods rely, for their polynomial time bound, on the initial subgraphs having only a constant number of components. Experiments performed by the authors of these methods seemed to confirm that randomly chosen point sets displayed this desired property. We show that there exist point sets where the number of components is linear in n. In fact, the expected number of components in either graph on a randomly chosen point set is linear in n, and the probability of the number of components exceeding some constant times n tends to one.

A Study of the Role of Modules in the Failure of Systems

1991 ◽  
Vol 5 (2) ◽  
pp. 215-227 ◽  
Author(s):  
Emad El Neweihi ◽  
Jayaram Sethuraman
Keyword(s):  
Optimal Allocation ◽  
System Failure ◽  
Coherent Systems ◽  
Expected Number ◽  
Number Of Components ◽  
Monotonicity Properties

Since the introduction of the concept of coherent systems and the description of the reliability of such systems in terms of the reliabilities of the components, the concept of importance of a component has created a new and fruitful area of research. Two distinct concepts of importance can be found in the literature. We take the view that the importance of a component or a module that is part of a system can be derived directly from the role of the component or the module in the failure of the system. Here again, it is possible that there will be several definitions of role. In this paper we define the role of a module (or component) to be the probability that the module is among all the modules (or components) that failed at the time of system failure. The role of a module depends on the structure of the system in terms of the modules, the structure of the module in terms of its components and the distribution of lifetimes of the components. In this paper we study the role of a module under several structures and distributions for lifetimes. We establish various monotonicity properties and indicate applications of these properties to optimal allocation. Another quantity that describes the nature of the components in sustaining the system is the number of components that fail at the time of the failure of the system. We establish monotonicity properties for the expected number of failed components and also indicate applications to optimal allocation.

scholarly journals On the most expected number of components for random links

2017 ◽  
Vol 69 (4) ◽  
pp. 637-641
Author(s):  
Kazuhiro Ichihara ◽  
Ken-ichi Yoshida
Keyword(s):  
Expected Number ◽  
Number Of Components
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