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SP2 MAXIMUM SET
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CoveringHitting, and Splitting
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CoveringHitting, and Splitting
-
I
NSTANCE
:
Set
, where
X
,
Y
, and
Z
are disjoint.
-
S
OLUTION
:
A matching for
T
, i.e., a subset
such that no elements
in
M
agree in any coordinate.
-
M
EASURE
:
Cardinality of the matching, i.e.,
|M|
.
-
Good News:
Approximable within 3/2
for any
[
182
].
-
Bad News:
A
PX
-complete [
198
].
-
Comment:
Transformation from M
AXIMUM
3-S
ATISFIABILITY
.
Admits a PTAS for `planar' instances [
278
].
Variation in which the number of occurrences of any element in
X
,
Y
or
Z
is bounded by a constant
B
is A
PX
-complete for
[
198
].
The generalized Maximum
k
-Dimensional Matching problem is
approximable within
for any
[
150
].
The constrained variation in which the input is extended with a subset
S
of
T
, and the problem is to find the 3-dimensional matching
that contains the largest number of elements from
S
,
is not approximable within
for some
[
352
].
-
Garey and Johnson:
SP1
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997