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Velocity and Distance of Neighbourhood Sequences
András Hajdu 1 and Lajos Hajdu 2
Acta Cybernetica 16 (2003) 133-145.
Abstract:
Das et al. [#!nseq!#] defined the notion of periodic
neighbourhood sequences. They also introduced a natural
ordering relation 
for such sequences.
Fazekas et al. [#!genseq!#] generalized the concept of
neighbourhood sequences, by dropping periodicity. They
also extended the ordering to these generalized
neighbourhood sequences. The relation has some unpleasant properties (e.g., it is not
a complete ordering). In certain applications it can be
useful to compare any two neighbourhood sequences. For
this purpose, in the present paper we introduce a
norm-like concept, called velocity, for neighbourhood
sequences. This concept is in very close connection with
the natural ordering relation. We also define a metric
for neighbourhood sequences, and investigate its
properties.
Footnotes
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen P.O.Box 12. Email: hajdua@math.klte.hu Research supported by the OTKA grant T032361.
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen P.O.Box 12. Email: hajdul@math.klte.hu Research supported in part by the Netherlands Organization for Scientific Research (NWO), the Hungarian Academy of Sciences, by grants T029330 and F034981 of the Hungarian National Foundation for Scientific Research (HNFSR), and by the FKFP grant 3272-13/066/2001.
Web administrator 2003-10-13