Affiliation:
1. Computer Science Department, Stanford University, Stanford, CA
Abstract
In the bin-packing problem a list
L
of
n
numbers are to be packed into unit-capacity bins. For any algorithm
S
, let
r
(
S
) be the maximum ratio
S
(
L
)/
L
*
for large
L
*
, where
S
(
L
) denotes the number of bins used by
S
and
L
*
denotes the minimum number needed. An on-line
Ο
(
n
log
n
)-time algorithm RFF with
r
(RFF) = 5/3 and an off-line polynomial-time algorithm RFFD with
r
(RFFD) ≤ 11/9 - ε for some fixed ε > 0, are given. These are strictly better, respectively, than two prominent algorithms: the First-Fit (FF), which is on-line with
r
(FF) = 17/10, and the First-Fit-Decreasing (FFD) with
r
(FFD) = 11/9. Furthermore, it is shown that any on-line algorithm
S
must have
r
(
S
) ≥ 3/2. The question, “How well can an
ο
(
n
log
n
)-time algorithm perform?” is also discussed. It is shown that in the generalized
d
-dimensional bin packing, any
ο
(
n
log
n
)-time algorithm
S
must have
r
(
S
) ≥
d
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
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