scholarly journals A story of diameter, radius, and (almost) Helly property

Networks ◽  
2020 ◽  
Author(s):  
Guillaume Ducoffe ◽  
Feodor F. Dragan
Keyword(s):  
Helly Property

scholarly journals An application of the Helly property to the partially ordered sets

1983 ◽  
Vol 35 (2) ◽  
pp. 185-198 ◽  
Author(s):  
Alain Quilliot
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Helly Property

scholarly journals An Efficient Algorithm for Helly Property Recognition in a Linear Hypergraph

2001 ◽  
Vol 46 ◽  
pp. 177-187 ◽  
Author(s):  
A. Bretto ◽  
H. Cherifi ◽  
S. Ubéda
Keyword(s):  
Efficient Algorithm ◽  
Helly Property ◽  
Linear Hypergraph

scholarly journals Computational aspects of the Helly property: a survey

2006 ◽  
Vol 12 (1) ◽  
pp. 7-33 ◽  
Author(s):  
Mitre C. Dourado ◽  
Fábio Protti ◽  
Jayme L. Szwarcfiter
Keyword(s):  
Property A ◽  
Helly Property ◽  
Computational Aspects

Rough Set-hypergraph-based Feature Selection Approach for Intrusion Detection Systems

2016 ◽  
Vol 66 (6) ◽  
pp. 612 ◽  
Author(s):  
M.R. Gauthama Raman ◽  
K. Kannan ◽  
S.K. Pal ◽  
V. S. Shankar Sriram
Keyword(s):  
Feature Selection ◽  
Intrusion Detection ◽  
Rough Set ◽  
Network Architecture ◽  
Cyber Attacks ◽  
Intrusion Detection Systems ◽  
Selection Algorithm ◽  
Feature Selection Algorithm ◽  
Detection Systems ◽  
Helly Property

Immense growth in network-based services had resulted in the upsurge of internet users, security threats and cyber-attacks. Intrusion detection systems (IDSs) have become an essential component of any network architecture, in order to secure an IT infrastructure from the malicious activities of the intruders. An efficient IDS should be able to detect, identify and track the malicious attempts made by the intruders. With many IDSs available in the literature, the most common challenge due to voluminous network traffic patterns is the curse of dimensionality. This scenario emphasizes the importance of feature selection algorithm, which can identify the relevant features and ignore the rest without any information loss. In this paper, a novel rough set κ-Helly property technique (RSKHT) feature selection algorithm had been proposed to identify the key features for network IDSs. Experiments carried using benchmark KDD cup 1999 dataset were found to be promising, when compared with the existing feature selection algorithms with respect to reduct size, classifier’s performance and time complexity. RSKHT was found to be computationally attractive and flexible for massive datasets.

scholarly journals Complexity results on graphs with few cliques

2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Bill Rosgen ◽  
Lorna Stewart
Keyword(s):  
Maximum Clique ◽  
Maximum Clique Problem ◽  
Polynomial Time Algorithms ◽  
Helly Property ◽  
Graph Class ◽  
International Audience ◽  
Edge Clique Cover ◽  
Np Complete ◽  
General Graphs ◽  
Clique Problem

Graphs and Algorithms International audience A graph class has few cliques if there is a polynomial bound on the number of maximal cliques contained in any member of the class. This restriction is equivalent to the requirement that any graph in the class has a polynomial sized intersection representation that satisfies the Helly property. On any such class of graphs, some problems that are NP-complete on general graphs, such as the maximum clique problem and the maximum weighted clique problem, admit polynomial time algorithms. Other problems, such as the vertex clique cover and edge clique cover problems remain NP-complete on these classes. Several classes of graphs which have few cliques are discussed, and the complexity of some partitioning and covering problems are determined for the class of all graphs which have fewer cliques than a given polynomial bound.

scholarly journals Mad families, P+(I)-ideals and ideal convergence

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3099-3108
Author(s):  
Jiakui Yu ◽  
Shuguo Zhang
Keyword(s):  
Necessary Condition ◽  
Ideal Convergence ◽  
Mad Families ◽  
Helly Property ◽  
Almost Disjoint ◽  
Almost Disjoint Families ◽  
The Ideal

Let I be an ideal on ?, the notion of I-AD family was introduced in [3]. Analogous to the well studied ideal I(A) generated by almost disjoint families, we introduce and investigate the ideal I(I-A). It turns out that some properties of I(I-A) depends on the structure of I. Denoting by a(I) the minimum of the cardinalities of infinite I-MAD families, several characterizations for a(I) ? ?1 will be presented. Motivated by the work in [23], we introduce the cardinality s?,?(I), and obtain a necessary condition for s?,?(I) = s(I). As an application, we show finally that if a(I) ? s(I), then BW property coincides with Helly property.

The (p,q)-Helly property and its application to the family of cliques of a graph

2003 ◽  
Vol 25 (7) ◽  
Author(s):  
Mitre Dourado ◽  
Fabio Protti ◽  
Jayme Szwarcfiter
Keyword(s):  
Helly Property ◽  
The Family

A Helly property of arcs

1989 ◽  
Vol 52 (3) ◽  
pp. 298-306 ◽  
Author(s):  
M. Van de Vel
Keyword(s):  
Helly Property

The Helly property on subfamilies of limited size

2005 ◽  
Vol 93 (2) ◽  
pp. 53-56 ◽  
Author(s):  
Mitre C. Dourado ◽  
Fábio Protti ◽  
Jayme L. Szwarcfiter
Keyword(s):  
Limited Size ◽  
Helly Property

scholarly journals Helly property in finite set systems

1993 ◽  
Vol 62 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Zsolt Tuza
Keyword(s):  
Set Systems ◽  
Helly Property ◽  
Finite Set
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