Communication complexity and association schemes

• Published in: 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060) p. 4
• Main Author: Tamm, U.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2000
• Subjects: Complexity theory; Computer science; Ear; Eigenvalues and eigenfunctions; Information theory; Mathematics; Polynomials
• ISBN: 9780780358577; 0780358570
• DOI: 10.1109/ISIT.2000.866294

Let D/sub 0/,..., D/sub n/ be the {0,l}-matrices forming an association scheme. Since /spl Sigma//sub k=0//sup n/D/sub k/ is the all-one matrix, a linear combination /spl Sigma//sub k=0//sup n/c/sub k/D/sub k/ can be regarded as the matrix (f(x,y))/sub x,y/ representing the function f defined by f(x,y)=c/sub k/ if (x,y) is in relation corresponding to matrix D/sub k/. Parameters of functions thus obtained may now be studied exploiting properties of the association scheme. One such parameter is the communication complexity C(f), which is the number of bits that two persons have to exchange in order to evaluate f(x,y), when initially one person only knows x and the other person only knows y.