1400 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



by restricting the freedom of choice allowed by PI and P2 is distinctly 

 superior to other alternatives. This variant is the one in which PI is 

 used but once to produce a single isolated fragment, which is then ex- 

 tended by repeated applications of P2. 



The successive steps of an efficient computational procedure, as ap- 

 plied to the example of Fig. 9, are shown in Fig. 10. The entries in the 

 top rows of the successive F tables are the distances from the connected 

 fragment to the unconnected terminals at each stage of fragment growth. 

 The entries in parentheses in the second rows of these tables indicate 

 the nearest neighbor in the fragment of the external terminal in question. 

 The computation is started by entering the first row of the distance 

 table into the F table (to start the growing fragment from Terminal 1). 

 A smallest entry in the F table is then selected (in this case, 2.8, asso- 

 ciated with External Terminal 4 and Internal Terminal 1). The link 1-4 

 is deleted from the F table and entered in the Solution Summary (Fig. 

 11). The remaining entries in the first stage F table are then compared 

 with the corresponding entries in the "4" row of the distance table 

 (reproduced beside the first F table). If any entry of this "added ter- 

 minal" distance table is smaller than the corresponding F table entry, 

 it is substituted for it, with a corresponding change in the parenthesized 

 index. (Since 3.4 is less than 5.2, the 3 column of the F table becomes 

 3.4/(4).) This process is repeated to yield the list of successive nearest 

 neighbors to the growing fragment, as entered in Fig. 11. The F and 

 "added terminal" distance tables grow shorter as the number of un- 

 connected terminals is decreased. 



This computational procedure is easily programmed for an automatic 

 computer so as to handle c^uite large-scale problems. One of its advan- 

 tages is its avoidance of checks for closed cycles and connectedness. 

 Another is that it never requires access to more than two rows of distance 

 data at a time — no matter how large the problem. 



SOLUTION SUMMARY 



Fig. 11 — Solution summary for computation of Fig. 10. 



