M. Naor, A. Orlitsky, and P. Shor, "Three results on interactive communication, " IEEE Transactions on Information Theory, vol. 39, no. 5, pp. 1608--1615, September 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the problems: Do restrictions on the size or structure of the key space help Alice and Bob to agree while exchanging substantially fewer than n bits We treat questions of secrecy and channel noise as secondary, regarding them as factors that can make communication expensive. Orlitsky and others [24, 21, 22, 23, 20] have studied communication complexity in settings where Alice observes a random variable X, Bob observes a random variable Y (often dependent on X) and the object is for them to exchange single outcomes each has seen. For example, Y may select two teams i and j from a league S = f1; ....

M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Trans. Info. Thy., 39:1608--1615, 1993.

....using the optimal protocol for f . Can we do better by considering all components simultaneously We shall provide a simple example for a function where C(f) 2 but C(f n ) #n log 2 3#. The measure lim sup n## 1 n C(f n ) is also called amortized communication complexity (see [17] or [31]) Direct sum methods in communication complexity are useful tools in separating complexity classes. Further applications are the comparison of lower bound techniques and the study of their power (how large can be the gap between the lower bound and the communication complexity) The intuition is ....

....to the componentwise evaluation of the function f n for basic functions f : 0, 1 m 0, 1 m # 0, 1 . They conjectured that the amortized communication complexity 1 n lim sup n## C(f n ) cannot di#er from C(f) by more than O(log m) bits. This was further studied in [17] cf. also [31]) COMMUNICATION COMPLEXITY OF FUNCTIONS ON DIRECT SUMS 599 where a partial function is presented with deterministic communication complexity C(f) #(log(m) but amortized complexity O(1) and also randomized protocols are studied. Here simultaneous computations can save a lot of communication ....

M. Naor, A. Orlitsky, and P. Shor, "Three results on interactive communication ", IEEE Trans. Inform. Theory 39, no. 5, 1993, 1608 - 1615.

....the problems: Do restrictions on the size or structure of the key space help Alice and Bob to agree while exchanging substantially fewer than n bits We treat questions of secrecy and channel noise as secondary, regarding them as factors that can make communication expensive. Orlitsky and others [24, 21, 22, 23, 20] have studied communication complexity in settings where Alice observes a random variable X, Bob observes a random variable Y (often dependent on X) and the object is for them to exchange single outcomes each has seen. For example, Y may select two teams i and j from a league S = f 1; ....

M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Trans. Info. Thy., 39:1608--1615, 1993.

....the problems: Do restrictions on the size or structure of the key space help Alice and Bob to agree while exchanging substantially fewer than n bits We treat questions of secrecy and channel noise as secondary, regarding them as factors that can make communication expensive. Orlitsky and others [OG90, Orl90, Orl91b, Orl91a, Orl92, NOS93] have studied communication complexity in settings where Alice observes a random variable X , Bob observes a random variable Y (often dependent on X) and the object is for them to exchange single outcomes each has seen. For example, Y may select two teams i and j from a league S = f 1; ....

M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Trans. Info. Thy., 39:1608--1615, 1993.

....instance. Subsection 3.2 shows another family of graphs for which slightly weaker results hold. For interactive communication, where the communicators are allowed to communicate back and forth, similar results were established by Feder, Kushilevitz, and Naor [7] and by Naor, Orlitsky, and Shor [16]. The graphs used to derive the above results have (G) which is merely logarithmic in the graph s size and therefore the implied source has oe (1) which are only about log log jX j. The same holds for the afore mentioned interactive communication results. Dual sources requiring a large number ....

M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Transactions on Information Theory, 39(5):1608--1615, September 1993.

....sent by the client plus the number of black box queries is at least n. 1. 4 Previous and related work The question of sending a string x from a client to a server, where the server has some information about x unknown to the client, has a long history in the area known as interactive communication [11, 14, 16, 15, 17, 18, 19, 21]. Here, it is typically assumed that a pair (x; y) is drawn from a joint probability distribution D p over pairs (x; y) where D p is known to both the client and the server in advance. The string x is given to the client, the string y is given to the server, and the task is to communicate the ....

A. O. M. Naor and P. Shor. Three results on interactive communication. IEEE Trans. on Information Theory, 39(5):1608--1615, 1993.

....instance. Subsection 3.2 shows another family of graphs for which slightly weaker results hold. For interactive communication, where the communicators are allowed to communicate back and forth, similar results were established by Feder: Kushilevitz, and Naor [7] and by Naor, Orlitsky, and Shot [16]. The graphs used to derive the above results have X(G) which is merely logarithmic in the graph s size and therefore the implied source has a ( which are only about log log IX[ The same holds br the afore mentioned interactive communication results. Dual sources requiring a large number of ....

M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Transactions on InJbrmation Theory, 39(5):1608 1615, September 1993.

....requires arbitrarily many bits, but multiple instances require at most two bits per instance. For interactive communication, where the communicators are allowed to communicate back and forth, similar results were established by Feder, Kushilevitz, and Naor [5] and by Naor, Orlitsky, and Shor [12]. The directed line graphs used to derive the above results have (G) which is merely logarithmic in the graph s size and therefore the implied source has oe (1) which are only about log log jX j. The same holds for the afore mentioned interactive communication results. Dual sources requiring a ....

M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Transactions on Information Theory, 39(5):1608--1615, September 1993.

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M. Naor, A. Orlitsky, and P. Shor, "Three results on interactive communication, " IEEE Transactions on Information Theory, vol. 39, no. 5, pp. 1608--1615, September 1993.

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