3.6. Construct and change an algorithm

Specify the required answer → construct its obtaining procedure → share or summarize only what the answer permits → bound cost and error → use the result → revise the changed dependency.

CMP.1 builds effective conversions and answer recovery when another solver can help. CMP.2 constructs a recurrence; CMP.3 chooses reuse and order. A mathematical construction or the formulation in MMP supplies their intended objects and answer conditions. It does not supply an algorithm merely by defining the answer.

The connected CMP example shows how a relaxed bound can finish a search for one best selection. Asking for every equally good selection changes which branches may be discarded and what a shared table must retain. CMP.4 supplies the exclusion rule, CMP.5 the bound and CMP.10 the representation comparison. The mathematical optimum can remain unchanged while its obtaining and output procedure changes.

If a weaker answer is acceptable, CMP.8 constructs an approximation and its error account. If the question concerns every possible algorithm under given access operations, CMP.11 constructs a lower bound rather than extrapolating the cost of one implementation. A changed input promise or tolerated error can reopen that limit. C.29.3 then connects the selected operations to physical execution where that contribution is needed.

These methods also support changing a way of working. A solver can move a contribution to another agent; a changed representation can make sharing possible; an interaction rule can prevent one contribution from invalidating another. C.29 and Method Engineering establish the correspondence to the actual working arrangement. They retain any physical or organizational requirement that the algorithmic argument did not address.