Problem of trace – one of the most labor-consuming in a common problem of automation of design of REA. It is connected with several factors, in particular with variety of ways of constructive and technological realization of connections, specific criteria of optimization and restriction are applied to each of which at the algorithmic solution of a task. From the mathematical point of view trace – the most difficult problem of a choice from huge number of versions of the optimum decision.
It is obvious that pair shift of tops of xg and xh will lead to change of number only of those GA(XA,UA connecting pieces) and GB(XB,UB) edges, which intsidentna to these tops. Total number of connecting edges between GA(XA,UA) and GB(XB,UB), incidental xg and xh, before shift of tops determine by a contiguity matrix as follows:
In other words as splittings parts of set of G into columns are considered, if any part from this set not empty; for any two parts crossing of a set of edges can be not empty; association of all parts is equal in accuracy column G.
where p and h (p) – serial number and a position of fixing of the motionless rp element. If, carry out the shift of ri and rj leading to reduction of criterion function on then run for search and shift of the following couple of elements, etc. Process comes to an end with receiving such option of placement for which further improvement due to pair shifts of elements is impossible.
Use of the described directed search reduces number of the analyzed placement options (in comparison with full search), but leads to loss of a guarantee of finding of a global extremum of criterion function.
The specified process proceeds until the set of X1 does not contain n of elements or accession of the next unallotted top of xj to a piece of G1(X1,U will not lead to violation of restriction on the number of external connections of a piece equal
After transformation of a piece of G10(X10,U1 process is repeated for formation of the pieces of the initial count second, third, etc. with only that difference that the tops which did not enter the previous pieces are subject to consideration.
The greatest distribution in algorithms of placement was gained by the first criterion that is explained by the following reasons: reduction of lengths of connections improves electric characteristics of the device, simplifies trace of printed-circuit boards; besides, it is rather simple in realization.
The main objective of trace is formulated as follows: according to the set scheme of connections to lay necessary conductors on the plane (a payment, a crystal, etc.) to realize the set technical connections taking into account in advance set restrictions. The main are restrictions on width of conductors and the minimum distances between them.