TY - JOUR

T1 - Choosing, Agreeing, and Eliminating in Communication Complexity

AU - Beimel, Amos

AU - Ben Daniel, Sebastian

AU - Kushilevitz, Eyal

AU - Weinreb, Enav

N1 - Funding Information:
A preliminary version of this paper appeared in Proc. of the 37th International Colloquium on Automata, Languages and Programming (ICALP), Part I, volume 6198 of Lecture Notes in Computer Science, pages 451–462, Springer-Verlag, 2010. The first and second authors are partially supported by ISF Grant 938/09. The third and fourth authors are supported by ISF Grant 1310/06.

PY - 2014/3/1

Y1 - 2014/3/1

N2 - We consider several questions inspired by the direct-sum problem in (two-party) communication complexity. In all questions, there are k fixed Boolean functions f1,...,fk and each of Alice and Bob has k inputs, x1,...,xk and y1,...,yk, respectively. In the eliminate problem, Alice and Bob should output a vector σ1,...,σk such that fi(xi, yi) ≠ σi for at least one i (i.e., their goal is to eliminate one of the 2k output vectors); in the choose problem, Alice and Bob should return (i, fi(xi, yi)), for some i (i.e., they choose one instance to solve), and in the agree problem they should return fi(xi, yi), for some i (i.e., if all the k Boolean values agree then this must be the output). The question, in each of the three cases, is whether one can do better than solving one (say, the first) instance. We study these three problems and prove various positive and negative results. In particular, we prove that the randomized communication complexity of eliminate, of k instances of the same function f, is characterized by the randomized communication complexity of solving one instance of f.

AB - We consider several questions inspired by the direct-sum problem in (two-party) communication complexity. In all questions, there are k fixed Boolean functions f1,...,fk and each of Alice and Bob has k inputs, x1,...,xk and y1,...,yk, respectively. In the eliminate problem, Alice and Bob should output a vector σ1,...,σk such that fi(xi, yi) ≠ σi for at least one i (i.e., their goal is to eliminate one of the 2k output vectors); in the choose problem, Alice and Bob should return (i, fi(xi, yi)), for some i (i.e., they choose one instance to solve), and in the agree problem they should return fi(xi, yi), for some i (i.e., if all the k Boolean values agree then this must be the output). The question, in each of the three cases, is whether one can do better than solving one (say, the first) instance. We study these three problems and prove various positive and negative results. In particular, we prove that the randomized communication complexity of eliminate, of k instances of the same function f, is characterized by the randomized communication complexity of solving one instance of f.

KW - Communication complexity

KW - direct sum

KW - elimination

KW - selection

UR - http://www.scopus.com/inward/record.url?scp=84893978752&partnerID=8YFLogxK

U2 - 10.1007/s00037-013-0075-7

DO - 10.1007/s00037-013-0075-7

M3 - Article

AN - SCOPUS:84893978752

SN - 1016-3328

VL - 23

SP - 1

EP - 42

JO - Computational Complexity

JF - Computational Complexity

IS - 1

ER -