TY - CHAP
T1 - An improved communication-randomness tradeoff
AU - Fürer, Martin
PY - 2004
Y1 - 2004
N2 - Two processors receive inputs X and Y respectively. The communication complexity of the function f is the number of bits (as a function of the input size) that the processors have to exchange to compute f(X, Y) for worst case inputs X and Y. The List-Non-Disjointness problem (X = (x1, . . . ,xn), Y = (y1, . . . , yn), xi, yj ∈ Z2n, to decide whether ∃j xj = yj) exhibits maximal discrepancy between deterministic n2 and Las Vegas (Θ(n)) communication complexity. Fleischer, Jung, Mehlhorn (1995) have shown that if a Las Vegas algorithm expects to communicate Ω(n log n) bits, then this can be done with a small number of coin tosses. Even with an improved randomness efficiency, this result is extended to the (much more interesting) case of efficient algorithms (i.e. with linear communication complexity). For any R ∈ ℕ, R coin tosses are sufficient for O(n + n2/2R) transmitted bits.
AB - Two processors receive inputs X and Y respectively. The communication complexity of the function f is the number of bits (as a function of the input size) that the processors have to exchange to compute f(X, Y) for worst case inputs X and Y. The List-Non-Disjointness problem (X = (x1, . . . ,xn), Y = (y1, . . . , yn), xi, yj ∈ Z2n, to decide whether ∃j xj = yj) exhibits maximal discrepancy between deterministic n2 and Las Vegas (Θ(n)) communication complexity. Fleischer, Jung, Mehlhorn (1995) have shown that if a Las Vegas algorithm expects to communicate Ω(n log n) bits, then this can be done with a small number of coin tosses. Even with an improved randomness efficiency, this result is extended to the (much more interesting) case of efficient algorithms (i.e. with linear communication complexity). For any R ∈ ℕ, R coin tosses are sufficient for O(n + n2/2R) transmitted bits.
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U2 - 10.1007/978-3-540-24698-5_48
DO - 10.1007/978-3-540-24698-5_48
M3 - Chapter
AN - SCOPUS:35048900974
SN - 3540212582
SN - 9783540212584
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 444
EP - 454
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
A2 - Farach-Colton, Martin
PB - Springer Verlag
ER -