L-reduction

In computer science, particularly the study of approximation algorithms, an L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserving reduction. L-reductions in studies of approximability of optimization problems play a similar role to that of polynomial reductions in the studies of computational complexity of decision problems.

The term L reduction is sometimes used to refer to log-space reductions, by analogy with the complexity class L, but this is a different concept.

Definition

Let A and B be optimization problems and c_A and c_B their respective cost functions. A pair of functions f and g is an L-reduction if all of the following conditions are met:

Reduction

Reduction, reduced, or reduce may refer to:

Science

Chemistry

Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A reduction from one problem to another may be used to show that the second problem is at least as difficult as the first.

Intuitively, problem A is reducible to problem B if an algorithm for solving problem B efficiently (if it existed) could also be used as a subroutine to solve problem A efficiently. When this is true, solving A cannot be harder than solving B. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, etc.).

We write A ≤_m B, usually with a subscript on the ≤ to indicate the type of reduction being used (m : mapping reduction, p : polynomial reduction).

The mathematical structure generated on a set of problems by the reductions of a particular type generally forms a preorder, whose equivalence classes may be used to define degrees of unsolvability and complexity classes.

Redox

Redox is a contraction of the name for chemical reduction-oxidation reaction. A reduction reaction always occurs with an oxidation reaction. Redox reactions include all chemical reactions in which atoms have their oxidation state changed; in general, redox reactions involve the transfer of electrons between chemical species. The chemical species from which the electron is stripped is said to have been oxidized, while the chemical species to which the electron is added is said to have been reduced. Oxygen is not necessarily included in such reactions as other chemical species can serve the same function.

The term "redox" comes from two concepts involved with electron transfer: reduction and oxidation. It can be explained in simple terms:

Although oxidation reactions are commonly associated with the formation of oxides from oxygen molecules, these are only specific examples of a more general concept of reactions involving electron transfer.