2006 | OriginalPaper | Buchkapitel
Quadratic Programming and Combinatorial Minimum Weight Product Problems
verfasst von : Walter Kern, Gerhard Woeginger
Erschienen in: Algorithms and Complexity
Verlag: Springer Berlin Heidelberg
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We present a fully polynomial time approximation scheme (FPTAS) for minimizing an objective (
a
T
x
+
γ
)(
b
T
x
+
δ
) under linear constraints
Ax
≤
d
. Examples of such problems are combinatorial minimum weight product problems such as, e.g., the following: Given a graph
G
=(
V
,
E
) and two edge weights
${\bf a, b}: E \to {\mathbb R}_{+}$
find an
s
–
t
path
P
that minimizes
a
(
P
)
b
(
P
), the product of its edge weights relative to
a
and
b
.
AMS-Class:
90C20, 90C26, 90C27.