Name
Title | ||
|---|---|---|
Separating deterministic from nondeterministic nof multiparty communication complexity |
Abstract | ||
|---|---|---|
We solve some fundamental problems in the number-onforehead (NOF) k-party communication model. We show that there exists a function which has at most logarithmic communication complexity for randomized protocols with a one-sided error probability of 1/3 but which has linear communication complexity for deterministic protocols. The result is true for k = nO(1) players, where n is the number of bits on each players' forehead. This separates the analogues of RP and P in the NOF communication model. We also show that there exists a function which has constant randomized complexity for public coin protocols but at least logarithmic complexity for private coin protocols. No larger gap between private and public coin protocols is possible. Our lower bounds are existential and we do not know of any explicit function which allows such separations. However, for the 3-player case we exhibit an explicit function which has Ω(log log n) randomized complexity for private coins but only constant complexity for public coins. It follows from our existential result that any function that is complete for the class of functions with polylogarithmic nondeterministic k-party communication complexity does not have polylogarithmic deterministic complexity. We show that the set intersection function, which is complete in the number-in-hand model, is not complete in the NOF model under cylindrical reductions. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/978-3-540-73420-8_14 | ICALP |
Keywords | Field | DocType |
public coin protocol,logarithmic communication complexity,set intersection function,explicit function,nondeterministic nof multiparty communication,separating deterministic,randomized complexity,constant randomized complexity,linear communication complexity,logarithmic complexity,constant complexity,polylogarithmic deterministic complexity,communication complexity,error probability,communication model,lower bound | Intersection (set theory),Discrete mathematics,Average-case complexity,Combinatorics,Nondeterministic algorithm,Existential quantification,Computer science,Decision tree model,Models of communication,Communication complexity,Logarithm | Conference |
ISBN | Citations | PageRank |
3-540-73419-8 | 4 | 0.56 |
References | Authors | |
16 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Paul Beame | 1 | 2234 | 176.07 |
| Matei David | 2 | 55 | 5.11 |
| Toniann Pitassi | 3 | 2282 | 155.18 |
| Philipp Woelfel | 4 | 432 | 38.40 |