Ordered

Five books sorted correctly on a shelf: A B C D E

Assume the books A-E communicate via NFC. Each unit knows how to sort and to sort first alphabetically then numerically. Assume there are limitations on how far the books signals can travel, thus not all books will be able to communicate with all the others.

 A B C D E (A can communicate with BCD)
 B
 C
 D

 A B C D E (B can communicate with ACDE)
   A
   C
   D
   E

 A B C D E (etc.)
     A
     B
     D
     E

 A B C D E
       A
       B
       C
       E

 A B C D E
         A
         B
         C
         D

Summarize the responses.

A asks for B, C, and D, (meaning book A requests a list from each of books BCD for their list of titles they're able to communicate with.) B asks for A, C, D, and E. C asks for A, B, D, and E. D asks for A, B, C, and E. E asks for A, B, C, and D.

A asks for a list from B, C, and D. A gets:

 A A A (BCD each can communicate with A)
 B B   (CD communicate with B)
 C C   (BD communicate with C)
 D D   (BC communicate with D)
 E E E (BCD each communicate with E)

B asks for a list from A, C, D, and E. B gets:

 A A A
 B B B B
 C C C
 D D D 
 E E

C asks for A, B, D, and E. C gets:

 A A A
 B B B 
 C C C C 
 D D D 
 E E

D asks for A, B, C, and E. D gets:

 A A A
 B B B
 C C C 
 D D D D 
 E E 

E asks for A, B, C, and D. E gets:

 A A A
 B B B 
 C C C
 D D D
 E E E

the other books communicate their call numbers, and the center book should find all of the other call numbers near its own.