IJPAM: Volume 21, No. 3 (2005)

CLUSTERS IN METRIC SPACES

C.H. Jamison$^1$, C. Turner$^2$, G.E. Livesey$^3$,
H.A. Donegan$^4$, J.McC. Anderson$^5$
$^{1,2,5}$School of Electrical and Mechanical Engineering
University of Ulster
Co. Antrim, BT37 0QB, N. IRELAND, U.K.
$^1$e-mail: ch.jamison@ulster.ac.uk
$^{3}$School Education
University of Ulster
Co. Antrim, BT37 0QB, N. IRELAND, U.K.
$^4$School of Computing and Mathematics
University of Ulster
Co. Antrim, BT37 0QB, N. IRELAND, U.K.


Abstract.This paper describes 3 methods which outline the construction of clusters within a metric space. We can choose a different radius for each open ball around each of the points contained within the metric space. An added bonus of the 3 methods is that the density of the clusters (and sub-clusters from which they are constructed) can be established using a straightforward calculation. There are many possible applications for these methods and an immediate application to the area of egress complexity is outlined.

Received: April 28, 2005

AMS Subject Classification: 54E35

Key Words and Phrases: metric space, cluster, egress, egress complexity, route complexity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 3