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

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





2006 ◽  
Vol 12 (1) ◽  
pp. 7-33 ◽  
Author(s):  
Mitre C. Dourado ◽  
Fábio Protti ◽  
Jayme L. Szwarcfiter


2016 ◽  
Vol 66 (6) ◽  
pp. 612 ◽  
Author(s):  
M.R. Gauthama Raman ◽  
K. Kannan ◽  
S.K. Pal ◽  
V. S. Shankar Sriram

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.



2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Bill Rosgen ◽  
Lorna Stewart

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.



Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3099-3108
Author(s):  
Jiakui Yu ◽  
Shuguo Zhang

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.



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


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


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


1993 ◽  
Vol 62 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Zsolt Tuza


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