TY - GEN

T1 - Partition arguments in multiparty communication complexity

AU - Draisma, Jan

AU - Kushilevitz, Eyal

AU - Weinreb, Enav

PY - 2009/11/12

Y1 - 2009/11/12

N2 - Consider the "Number in Hand" multiparty communication complexity model, where k players P 1,...,P k holding inputs (respectively) communicate in order to compute the value f(x 1,...,x k ). The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we study the power of the partition arguments method. Our two main results are very different in nature: (i) For randomized communication complexity we show that partition arguments may be exponentially far from the true communication complexity. Specifically, we prove that there exists a 3-argument function f whose communication complexity is Ω(n) but partition arguments can only yield an Ω(log n) lower bound. The same holds for nondeterministic communication complexity. (ii) For deterministic communication complexity, we prove that finding significant gaps, between the true communication complexity and the best lower bound that can be obtained via partition arguments, would imply progress on (a generalized version of) the "log rank conjecture" of communication complexity.

AB - Consider the "Number in Hand" multiparty communication complexity model, where k players P 1,...,P k holding inputs (respectively) communicate in order to compute the value f(x 1,...,x k ). The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we study the power of the partition arguments method. Our two main results are very different in nature: (i) For randomized communication complexity we show that partition arguments may be exponentially far from the true communication complexity. Specifically, we prove that there exists a 3-argument function f whose communication complexity is Ω(n) but partition arguments can only yield an Ω(log n) lower bound. The same holds for nondeterministic communication complexity. (ii) For deterministic communication complexity, we prove that finding significant gaps, between the true communication complexity and the best lower bound that can be obtained via partition arguments, would imply progress on (a generalized version of) the "log rank conjecture" of communication complexity.

UR - http://www.scopus.com/inward/record.url?scp=70449111704&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02927-1_33

DO - 10.1007/978-3-642-02927-1_33

M3 - Conference contribution

AN - SCOPUS:70449111704

SN - 3642029264

SN - 9783642029264

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 390

EP - 402

BT - Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings

T2 - 36th International Colloquium on Automata, Languages and Programming, ICALP 2009

Y2 - 5 July 2009 through 12 July 2009

ER -