Error bounds on the probabilistically optimal problem solving strategy

TL;DR

This paper analyzes how swapping the order of solution candidates affects the efficiency of an optimal probabilistic problem solving strategy, providing bounds on the resulting errors in general and specific systems.

Contribution

It introduces bounds on the error caused by reordering solution candidates in an optimal probabilistic search strategy, including special case analyses.

Findings

Derived general bounds on reordering errors.

Analyzed three specific systems with restrictions.

Provided insights into problem solving efficiency impacts.

Abstract

We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with respect to this optimal strategy on the problem solving effectivity (i.e., the solution candidates examined as well as time spent before solving the problem). Such interchange can happen in the applications with only partial information available. We derive bounds on these errors in general as well as in three special systems in which we impose some restrictions on the solution candidates.