Constructing datatype-generic fully polynomial-time approximation schemes using generalised thinning

Authors:
Shin-Cheng Mu;Yu-Han Lyu;Akimasa Morihata
Affiliations:
Academia Sinica, Taipei, Taiwan Roc;Academia Sinica, Taipei, Taiwan Roc;Tohoku University, Tokyo, Japan
Venue:
Proceedings of the 6th ACM SIGPLAN workshop on Generic programming
Year:
2010

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Abstract

The fully polynomial-time approximation scheme (FPTAS) is a class of approximation algorithms 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.