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approximation scheme (
FPTAS) is an
algorithm for
finding approximate solutions to
function problems,
especially optimization problems. An
FPTAS takes as input...
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algorithm FPTAS is input: ε ∈ (0,1] a list A of n items,
specified by
their values, v i {\displaystyle v_{i}} , and
weights output: S' the
FPTAS solution...
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those in APX) or even up to any
approximation ratio (those in PTAS or
FPTAS).
There are many
classes of approximability, each one
enabling approximation...
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approximation scheme or
FPTAS,
which requires the
algorithm to be
polynomial in both the
problem size n and 1/ε.
Unless P = NP, it
holds that
FPTAS ⊊ PTAS ⊊ APX...
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objective function cannot have a
fully polynomial-time
approximation scheme (or
FPTAS)
unless P = NP. However, the
converse fails: e.g. if P does not
equal NP...
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following subclasses according to
their approximability: NPO(I):
Equals FPTAS.
Contains the
Knapsack problem. NPO(II):
Equals PTAS.
Contains the Makespan...
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polynomial in the size of the
input and 1/η (rather than log(1/η)), is
called an
FPTAS. In most
indicating instruments, the
accuracy is
guaranteed to a certain...
- NP-complete in 1975 by Lueker. Both the
bounded and
unbounded variants admit an
FPTAS (essentially the same as the one used in the 0-1
knapsack problem). If the...
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worst case, its
approximation ratio is 8/7. The
subset sum
problem has an
FPTAS which can be used for the
partition problem as well, by
setting the target...
- ) m − 1 ) {\displaystyle O(n\cdot (n^{2}/\epsilon )^{m-1})} . It is an
FPTAS if m is fixed. For m=2, the run-time
improves to O ( n 2 / ϵ ) {\displaystyle...
