B.S.T.J. Briefs: A Table Look Up Approach to Loop Switching

s = max,, Z) ,-,·). We consider a PQl factorization of D with P and Q matrices each of order n X ns. The zth row of P, P, , is zero everywhere except in positions (s(i -- 1) + 1) to si where it is one. The tth row of Q, Q{ , is constructed as follows: for every j, there are exactly Dj{ l's in positions (s(j -- 1) + 1) to sj with the rest of the entries of Q{ equal to zero. * The scalar product of two binary streams of equal length is the number of places they both have a "one". 2095 2096 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1972 2s 3s 2 I 1 1 . . . 1 0 - - - 0 0 ··· 0 ··· S ns 0 ··· 0 p = 0 ··· 0 1 ··· 1 0 ··· 0 0 · · · 0 0 · · · 0 0 · · · 0 ··· 1 · · · 1 s 1 0 ··· 0 D i2 2s D13 3s ^ 1 I 1 ... 1 ... o 1 1 · ·· 0 0 1 ··· 1 ··· 0 ns ^ I . 1 ... 1 ... 0 1 ... 1 ... o 0 0. Dln Q = 1 · · · 10 0 1 . . . 10 l . . . 1 . . . 0 1 · ·. 1 . · · 0 Obviously the length of addresses in this scheme is ns. The P matrix defined above, rows of which are addresses to be prefixed onto messages, is the same for all graphs with diameter s. The Q matrix, rows of which are stored in the loops in the network, contains the information that identifies a particular graph. As will be discussed further, a simple mechanization of this scheme reveals that it is essentially an obvious table look up scheme. In a table look up scheme, each loop has stored the distance between it and every other loop in the networks, and each address essentially provides a signal to look up or read out a particular distance that is stored.