SHORTEST COXXECTIOX XETWOUKS 1391 



interest in cjuite different contexts from those in which the basic prob- 

 lem had its genesis. 



II. CONSTRUCTION PRINCIPLES FOR SHORTEST CONNECTION NETWORKS 



In order to state the rules for solution of the basic problem concisely, 

 it is necessary to introduce a few, almost self-explanatory, terms. An 

 isolated terminal is a terminal to which, at a given stage of the construc- 

 tion, no connections have yet been made. (In Fig. 2, terminals 2, 4, and 

 9 are the only isolated ones.) A fragment is a terminal subset connected 

 by direct links, between members of the subset. (In Fig. 2, 8-3, 1-6-7-5, 

 5-6-7, and 1-6 are some of the fragments; 2-4, 4-8-3, 1-5-7, and 1-7 are 



9 



o 



2 

 O 



07 



04 



Fig. 2 — Partial connection network. 



not fragments.) The distance of a terminal from a fragment of which it 

 is not an element is the minimum of its distances from the individual 

 terminals comprising the fragment. An isolated fragment is a fragment 

 to which, at a given stage of the construction, no external connections 

 have been made. (In Fig. 2, 8-3 and 1-6-7-5 are the only isolated frag- 

 ments.) A nearest neighbor of a terminal is a terminal whose distance 

 from the specified terminal is at least as small as that of an}^ other. A 

 nearest neighbor of a fragment, analogously, is a terminal whose distance 

 from the specified fragment is at least as small as that of an}^ other. 



The two fundamental construction principles (PI and P2) for shortest 

 connection networks can now be stated as follows: 



Principle 1 — Any isolated ierminal can he connected to a nearest 

 neighbor. 



Principle 2 — Any isolated fragment can be connected to a nearest 

 neighbor by a shortest available link. 



For example, the next steps in the incomplete construction of Fig. 2 

 could be any one of the following: 



(1) add link 9-2 (PI applied to Teiin. 9) 



