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On variable sized vector packing
Leah Epstein 1
Acta Cybernetica 16 (2003) 47-56.
Abstract:
One of the open problems in on-line packing is the gap
between the lower bound 
and the upper bound 
for vector packing of 
-dimensional items into -dimensional bins. We address a more general
packing problem with variable sized bins. In this
problem, the set of allowed bins contains the
traditional "all-
" vector, but also a finite number
of other -dimensional vectors. The study of this
problem can be seen as a first step towards solving the
classical problem. It is not hard to see that a simple
greedy algorithm achieves competitive ratio for every set of bins. We show that for all
small 
there exists a set
of bins for which the competitive ratio is 
. On the other hand we show that there exists a
set of bins for which every deterministic or randomized
algorithm has competitive ratio 
. We also study one special case for
.
Footnotes
School of Computer Science, The Interdisciplinary Center, Herzliya, Israel. Email: lea@idc.ac.il Research supported in part by the Israel Science Foundation, (grant No. 250/01-1).
Web administrator 2003-10-13