TY - JOUR
T1 - Approximate by thinning
T2 - Deriving fully polynomial-time approximation schemes
AU - Mu, Shin Cheng
AU - Lyu, Yu Han
AU - Morihata, Akimasa
N1 - Publisher Copyright:
© 2014 Elsevier B.V. All rights reserved.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - The fully polynomial-time approximation scheme (FPTAS) is a class of approximation algorithms for optimisation problems that is able to deliver an approximate solution within any chosen ratio in polynomial time. By generalising Bird and de Moor's Thinning Theorem to a property between three orderings, we come up with a datatype-generic strategy for constructing fold-based FPTASs. Greedy, thinning, and approximation algorithms can thus be seen as a series of generalisations. Components needed in constructing an FPTAS are often natural extensions of those in the thinning algorithm. Design of complex FPTASs is thus made easier, and some of the resulting algorithms turn out to be simpler than those in previous works.
AB - The fully polynomial-time approximation scheme (FPTAS) is a class of approximation algorithms for optimisation problems that is able to deliver an approximate solution within any chosen ratio in polynomial time. By generalising Bird and de Moor's Thinning Theorem to a property between three orderings, we come up with a datatype-generic strategy for constructing fold-based FPTASs. Greedy, thinning, and approximation algorithms can thus be seen as a series of generalisations. Components needed in constructing an FPTAS are often natural extensions of those in the thinning algorithm. Design of complex FPTASs is thus made easier, and some of the resulting algorithms turn out to be simpler than those in previous works.
KW - Approximation algorithms
KW - Program derivation
UR - http://www.scopus.com/inward/record.url?scp=84916939616&partnerID=8YFLogxK
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U2 - 10.1016/j.scico.2014.07.001
DO - 10.1016/j.scico.2014.07.001
M3 - Article
AN - SCOPUS:84916939616
VL - 98
SP - 484
EP - 515
JO - Science of Computer Programming
JF - Science of Computer Programming
SN - 0167-6423
IS - P4
ER -