TY - CHAP

T1 - An improved communication-randomness tradeoff

AU - Fürer, Martin

PY - 2004/1/1

Y1 - 2004/1/1

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 -