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From: Stephan Ceram on 18 Jan 2010 17:40
Hi,

I'm looking for a formal definition of the following problem that I first
describe in words:

Let's assume I have a set of 'n' algorithms 'a' represented by the set
'A'. Furthermore, each algorithm 'a' \in 'A' can be configured by 'm'
different parameters 'P=(p_1,...,p_n)' (I represent the parameters for a
particular algorithm by a vector). The set of possible parameter vectors
'P' is represented by 'PAR'. Moreover, there are different inputs 'e' \in
'E' that can be processed by each algorithm 'a', resulting in some cost
'cost'.

The problem is now to find for a given input 'i' the algorithm 'a' with
a particular parameter configuration (i.e. concrete values for each
parameter) such that some given cost function is maximized. So basically
this is a simple maximization problem that I would like to express
formally. This is my suggestion:

---
Given a set of algorithms 'a' \in 'A' and a set of parameter vectors
'P' \in 'PAR', with 'P_i=(p^i_1,...,p^i_m)' being the parameter
vector for algorithm 'a_i' and 'i,m=1,...,N'. Moreover, each parameter
vector can be assigned a parameter configuration 'C=(p_1->c_1,...,
p_m->c_m)'.
For a given input 'e', the problem is to find an algorithm 'a' with a
valid parameter configuration 'C', such that 'a' maximizes the given
cost function.
----

Is this problem specification correct and complete? Do you see any ways
to improve it?

Thank you.

Stephan
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