In computability and in complexity theory reductions are widely used for mapping sets into sets in order to prove undecidability or hardness results. In the study of the approximate solvability of hard discrete optimization problems, suitable kinds of reductions, called approximation preserving reductions, can also be used to transfer from one problem to another either positive results (solution techniques) or negative results (non-approximability results). In this paper various kinds of approximation preserving reductions are surveyed and their properties discussed. The role of completeness under approximation preserving reductions is also analyzed and its relationship with hardness of approximability is explained. (c) 2005 Elsevier B.V. All rights reserved.
Reductions, completeness and the hardness of approximability / Ausiello, Giorgio; V., Th Paschos. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - 172:3(2006), pp. 719-739. [10.1016/j.ejor.2005.06.006]
Reductions, completeness and the hardness of approximability
AUSIELLO, Giorgio;
2006
Abstract
In computability and in complexity theory reductions are widely used for mapping sets into sets in order to prove undecidability or hardness results. In the study of the approximate solvability of hard discrete optimization problems, suitable kinds of reductions, called approximation preserving reductions, can also be used to transfer from one problem to another either positive results (solution techniques) or negative results (non-approximability results). In this paper various kinds of approximation preserving reductions are surveyed and their properties discussed. The role of completeness under approximation preserving reductions is also analyzed and its relationship with hardness of approximability is explained. (c) 2005 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
