Amortized communication complexity

The authors study the direct sum problem with respect to communication complexity: Consider a function f: D to (0, 1), where D contained in (0, 1)/sup n/*(0, 1)/sup n/. The amortized communication complexity of f, i.e. the communication complexity of simultaneously computing f on l instances, divided by l is studied. The authors present, both in the deterministic and the randomized model, functions with communication complexity Theta (log n) and amortized communication complexity O(1). They also give a general lower bound on the amortized communication complexity of any function f in terms of its communication complexity C(f).<<ETX>>

[1]  Noga Alon,et al.  Simple construction of almost k-wise independent random variables , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[2]  Ran Raz,et al.  Monotone circuits for matching require linear depth , 1990, STOC '90.

[3]  Nader H. Bshouty,et al.  On the extended direct sum conjecture , 1989, STOC '89.

[4]  János Komlós,et al.  Deterministic simulation in LOGSPACE , 1987, STOC.

[5]  János Komlós,et al.  Storing a sparse table with O(1) worst case access time , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[6]  Giulia Galbiati.  M. J. Fischer: On the Complexity of 2-Output Boolean Networks , 1981, Theor. Comput. Sci..

[7]  Quentin F. Stout,et al.  Meshes with multiple buses , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[8]  Moni Naor,et al.  Small-bias probability spaces: efficient constructions and applications , 1990, STOC '90.

[9]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[10]  H. S. WITSENHAUSEN,et al.  The zero-error side information problem and chromatic numbers (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[11]  Alfred V. Aho,et al.  On notions of information transfer in VLSI circuits , 1983, STOC.

[12]  Avi Wigderson,et al.  Monotone circuits for connectivity require super-logarithmic depth , 1990, STOC '88.

[13]  Nathan Linial,et al.  Graph products and chromatic numbers , 1989, 30th Annual Symposium on Foundations of Computer Science.

[14]  Wolfgang J. Paul.  Realizing Boolean Functions on Disjoint sets of Variables , 1976, Theor. Comput. Sci..

[15]  Kurt Mehlhorn,et al.  Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract) , 1982, STOC '82.

[16]  Alon Orlitsky.  Two messages are almost optimal for conveying information , 1990, PODC '90.