Alon Orlitsky. Interactive communication: Balanced distributions, correlated files, and average-case complexity. In IEEE Symposium on Foundations of Computer Science, pages 228--238, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of data reconciliation. Another model involves two hosts reconciling files (or strings) that differ by a bounded number of insertions, deletions, or modifications (collectively: edits ) The problem of efficient reconciliation under these circumstances, also known as the edit distance problem [13], has been extensively studied [14, 15] because of its connections to important fields such as file synchronization and pattern recognition. LeventeYn [16] pioneered work in this area by developing error correcting codes capable of correcting precisely these types of errors. Recently [17] also ....

Alan Orlitsky, "Interactive communication: Balanced distributions, correlated files, and average-case complexity.," in Proceedings of the 3nd Annual Symposium on Foundations of Computer Science, 1991, pp. 228-238.

....known joint prob ability distribution using a minimum communication complexity. Witsenhausen [10] followed by Alon and Orlitsky [11] show a connection between such random variable reconciliation and graph coloring, giving results analogous to those of Section 3.1 and 4.1. In addition, Orlitsky [12] showed how to use linear error correcting codes for a specific instance of data reconciliation. Another model involves two hosts reconciling files (or strings) that differ by a bounded number of insertions, deletions, or modifications (collectively: edits ) The problem of efficient ....

....the individual data items, and not their relative position, matters. Unlike other models, we also assume that reconciliation is agnostic to the roles of participating hosts, as explained in Section 2. Our results extend the bridge between coding theory and data reconciliation originally started in [12], providing statements of conditioned equivalence and corresponding bounds. 1.2 Organization We begin in Section 2 with a brief formal introduction of the three problems connected in this paper. Section 3 addresses the general problem of data verification, proving connections between graph ....

Alan Orlitsky, "Interactive communication of balanced distributions and correlated files," SIAM Journal on Discrete Mathematics, vol. 6, no. 4, pp. 548-564, November 1993.

....such a scenario. Also, while our definition assumes a single reference file 321 , there could be several similar files that might be helpful in communicating the contents of to the client, as discussed later. In the case of the file synchronization problem, many currently known protocols [49, 16, 35] consist of a single round of communication, where the client first sends a request with a limited amount of information about t 2 to the server, and the server then sends an encoding of the current file to the client. In the case of a multi round protocol, a standard model for communication ....

....also depend on the number of messages exchanged between the two parties (e. g, in rsync, two messages are exchanged) In this subsection, we describe the basic ideas underlying these approaches, and give an overview of known results, with emphasis on a few fundamental bounds presented by Orlitsky [35]. See [28, 17] and the references in [35] for some earlier results on this problem. The results in [35] are stated for a very general framework of pairs of random variables; in the following we give a slightly simplified presentation for the case of correlated (similar) files. Distance Measures: ....

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A. Orlitsky. Interactive communication of balanced distributions and of correlated files. SIAM Journal of Discrete Math, 6(4):548--564, 1993.

....to this simplified synchronization model. It is generally not the case that database differences for mobile systems can be modeled as non destructive corruptions. Instead, we need to allow for data to be added or deleted from anywhere within a database, as happens practically. Several sources [29, 30] have studied extended synchronization models in which the permitted corruptions include insertions, deletions, and modifications of database entries. Recently, Cormode, Paterson, S . ahinhalp, and Vishkin [31] provided a probabilistic solution for such synchronization when a bound on the number ....

Alon Orlitsky, "Interactive communication: Balanced distributions, correlated files, and average-case complexity.," in Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, 1991, pp. 228-- 238.

....to this simplified synchronization model. It is generally not the case that database differences for mobile systems can be modeled as non destructive corruptions. Instead, we need to allow for data to be added or deleted from anywhere within a database, as happens practically. Several sources [29, 30] have studied extended synchronization models in which the permitted corruptions include insertions, deletions, and modifications of database entries. Recently, Cormode, Paterson, S . ahinhalp, and Vishkin [31] provided a probabilistic solution for such synchronization when a bound on the number ....

Alon Orlitsky, "Interactive communication: Balanced distributions, correlated files, and average-case complexity.," in Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, 1991, pp. 228-- 238.

....to those of Section 3.1 and 4.1. Another model involves two hosts reconciling les (or strings) that di er by a bounded number of insertions, deletions, or modi cations (collectively: edits ) The problem of ecient reconciliation under these circumstances, also known as the edit distance problem [10], has been extensively studied [11, 12] because of its connections to important elds such as le synchronization and pattern recognition. Leven ste n [13] pioneered work in this area by developing error correcting codes capable of correcting precisely these types of errors. Recently [14] ....

Alon Orlitsky, \Interactive communication: Balanced distributions, correlated les, and average-case complexity.," in Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, 1991, pp. 228-238.

....there is no such stable indexing. Set reconciliation is more closely related to the edits problem, which is the problem of reconciling two strings where one string di ers from the other by a bounded number of edits, i.e. insertions or deletions. The edits problem was analyzed by Orlitsky [13], and Ev mievski [4] presented a probabilistic solution. An algorithm for solving the edits problem can be used to perform set reconciliation by treating the hosts sets as strings consisting of the set elements listed in lexicographic order. Missing elements then correspond to deletions and ....

Orlitsky, A. Interactive communication of balanced distributions and correlated les. SIAM Journal on Discrete Mathematics 6, 4 (November 1993), 548-564.

....large body of relevant work on interactive communication problems is detailed in [3, 4, 12, 15] and the many citations therein. These results mostly focus on theoretical bounds for exchange of information about two related random variables. The work most closely related to ours is that of Orlitsky [16], who considers from an information theoretic perspective the reconciliation of binary strings of a prescribed edit distance apart. Orlitsky analyzes and bounds how much communication is needed for this string reconciliation, leaving a concrete construction of a corresponding protocol as his ....

....attempt to find the intersection of their respective data sets. Similarly, one might imagine a client reconciling [resolving] with many different data sets, provided the client maintains its original data set as it reconciles [resolves] with each host. A related problem is the ff edits problem [16], which may be thought of as an ordered instance of the multi set reconciliation problem. In this problem, a host p has a string S p and another host has a string S q ; the strings are related in that one may be attained from the other using at most ff insertions or deletions, collectively called ....

Orlitsky, A. Interactive communication of balanced distributions and correlated files. SIAM Journal on Discrete Mathematics 6, 4 (November 1993), 548--564.

....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 [14, 17, 18, 19, 20, 21, 22, 25]. 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 5 to communicate the ....

A. Orlitsky. Interactive communication of balanced distributions and of correlated les. SIAM J. of Dis. Math, 6(4):548-564, 1993. 21

....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 [14, 17, 18, 19, 20, 21, 22, 25]. 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 5 to communicate the ....

A. Orlitsky. Interactive communication: balanced distributions, correlated les, and averagecase complexity. In Proc. 32nd IEEE Symposium on Foundations of Computer Science, pages 228-238, 1991.

.... In fact, this lower bound holds even if the protocol computes the Hamming distance with any constant probability, as shown by Pang and El Gamal [PG86] For more general, balanced measures 1 of string distance d(x; y) the first protocols for exchanging documents are explored by Orlitsky [Orl91] These protocols assume a fixed upper bound f on d(x; y) and they require the transmission of Omega Gamma f log n) bits for the Hamming distance. If d(x; y) f , then the protocols result in an error; if d(x; y) o(f) then we show in this paper that too many bits are transmitted. Metzner ....

....different pages between two copies of an updated file. It is assumed that the differences between pages are aligned with the page boundaries, effectively resulting in Hamming differences. They also assume a known upper bound f on the number of pages that are different, as per the framework in [Orl91] In particular [AGE94] describes a protocol based on error correcting codes; this protocol sends a single message of O(f log n) bits to correct up to f differences. Contributions. Our most interesting protocols involve only two rounds of communication. The first round involves estimating d(x; ....

[Article contains additional citation context not shown here]

A. Orlitsky. Interactive communication: Balanced distributions, correlated files, and average-case complexity. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 228--238. IEEE, October 1991.

....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 [12, 15, 16, 17, 18, 19, 20, 22]. 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. Orlitsky. Interactive communication of balanced distributions and of correlated files. SIAM J. of Dis. Math, 6(4):548--564, 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 [12, 15, 16, 17, 18, 19, 20, 22]. 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. Orlitsky. Interactive communication: balanced distributions, correlated files, and averagecase complexity. In Proc. 32nd IEEE Symposium on Foundations of Computer Science, pages 228--238, 1991.

....H . We have made our point that we are dealing with a covering problem. Special properties can sometimes yield better bounds than the general bound in the Covering Lemma. Finally we mention that Lov asz s Local Lemma has been used successfully by Orlitsky in coloring problems, for instance in [24]. It yields the following improvement of Coloring Lemma 1. Strengthened Coloring Lemma. Let H = V; E) be a hypergraph with D E = max E2E jEj L . If for some t 2 N e Delta D 2 E DV t 1; 1.4) then a coloring : V f1; 2; Lg exists with j Gamma1 (i) Ej t for all i = 1; ....

....D E Prob E2E AE 0 (and there exists the desired coloring) if D E t 1 eD E Delta D V : 1.7) The Covering Lemma can be strengthened in the same way. Since it is not used in this paper, we omit the details and refer to the analogous version for perfect hashing in Lemma 3 of [24]. VI. We recall previous work on interactive communication (see [21] 25] and [27] 29] addresses the case in which P E is to be informed about the vertex v 2 V and the case in which PV and P E communicate over the same binary noiseless channel and the total number of bits are counted. In ....

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A. Orlitsky, "Interactive communication, balanced distributions, correlated files, and average case complexity", Proc. 23rd Annual Symp. Foundations of Computer Sc., pp. 228--238, 1991.

....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; ....

A. Orlitsky. Interactive communication: balanced distributions, correlated files, and average-case complexity. In Proc. 32nd Annual IEEE Symposium on Foundations of Computer Science, pages 228--238, 1991.

....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. Orlitsky. Interactive communication of balanced distributions and of correlated files. SIAM J. of Dis. Math, 6(4):548--564, 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. Orlitsky. Interactive communication: balanced distributions, correlated files, and average-case complexity. In Proc. 32nd IEEE Symposium on Foundations of Computer Science, pages 228--238, 1991.

.... y extending the minterm and thus f(y) 0 with x i = 1 and y i = 0) Communication complexity of boolean relations is of intrinsic interest, and has been extended to probabilistic versions by Raz and Widgerson [RW89] Average case communication complexity has also been previously studied [O91], FKN91] but in a different context. Lower bounds on the communication complexity for explicit functions can be used to derive lower bounds on worst case parallel time (circuit depth) While the notoriously hard problem of proving superlogarithmic parallel time bounds for explicit boolean ....

A. Orlitsky, Interactive Communication: Balanced Distributions, Correlated Files, and Average-Case Complexity, Proc. 32nd Symposium on the Foundations of Computer Science, October 1991, pp. 228 - 238.

....it is not known whether a constant number of messages are asymptotically optimum. Namely, whether there is an m such that for all (X; Y ) pairs, Cm (XjY ) C1 (XjY ) o( C1 (XjY ) We note that in the special case where the support set is balanced, 4 it has been recently shown [6] that three messages are asymptotically optimum for worst case complexity. A large discrepancy between the number of bits required with m and (m 1) messages occurs in worst case communication complexity. There, see [7] for precise definitions, PX knows X while P Y knows Y and wants to learn ....

A. Orlitsky. Interactive communication of balanced distributions and of correlated files. SIAM Journal of Discrete Mathematics, 6(4):548--564, November 1993.

....0, there is a balanced (X; Y ) pair such that C 2 2 C 3 Gamma o( C 3 ) c : Proof: Essentially, the result is already proven. Generate an (X; Y ) pair as described prior to Lemma 2. With probability approaching 1, and j are about n, while D(G) n 2 16 ln n . Hence, by Theorem 1 in [16], C 3 log n 3 log log n 11 ; 6) whereas Result 3 implies C 2 log D(G) 2 log n Gamma log ln n Gamma 4 : 7) There are however two technical difficulties. First, the conditions of Result 3 may not be met. G may have two edges that do not intersect. To overcome this, we can increase ....

....) be the largest asymptotic ratio between C i and C j for balanced (X; Y ) pairs. Then, R i;j = 8 : 2 if i = 1 or 2 1 otherwise. Namely, 1. The largest asymptotic ratio between C 1 and Cm is 2 for all m 2. This ratio is achieved for all m 2 by the projective plane problem (Lemma 2 in [16]) and for m 3 by the rooks problem (Example 2 in [16] see also open problems in Section 5) 2. As we just proved, the largest asymptotic ratio between C 2 and Cm is 2 for all m 3. 3. Since three messages are asymptotically optimal for all balanced pairs, the largest asymptotic ratio ....

[Article contains additional citation context not shown here]

A. Orlitsky. Interactive communication: Balanced distributions, correlated files, and average-case complexity. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 228--238, 1991.

....from each other. 2. X and Y , obtained from a noisy binary transmission or from a faulty memory, are n bit strings within a bounded Hamming distance from each other. 3. X and Y , modified versions of the same file, are binary strings within a small edit distance from each other. It is shown in [9] that for all balanced random pairs, one way communication requires at most twice the minimum number of bits: C 1 2 C1 1 : 2) This bound is almost tight. For all c there is a balanced pair such that C 1 2 C1 Gamma 6 c : The most interesting result in [9] is that for all balanced ....

....from each other. It is shown in [9] that for all balanced random pairs, one way communication requires at most twice the minimum number of bits: C 1 2 C1 1 : 2) This bound is almost tight. For all c there is a balanced pair such that C 1 2 C1 Gamma 6 c : The most interesting result in [9] is that for all balanced pairs, C 3 log 3 log log 11 : Hence, although the informant, PX , does not know Y , the number of bits needed to convey X to P Y is only negligibly larger than would be required if PX knew Y in advance. Furthermore, three messages are asymptotically optimum: ....

A. Orlitsky. Interactive communication of balanced distributions and of correlated files. SIAM Journal of Discrete Mathematics, 6(4):548--564, November 1993.

No context found.

Alon Orlitsky. Interactive communication: Balanced distributions, correlated files, and average-case complexity. In IEEE Symposium on Foundations of Computer Science, pages 228--238, 1991.

No context found.

A. Orlitsky, \Interactive communication of balanced distributions and of correlated les," SIAM J. Discret. Math., vol. 6, pp. 548-564, November 1993.

No context found.

A. Orlitsky, "Interactive communication of balanced distributions and correlated files," SIAM Journal on Discrete Mathematics, vol. 6, no. 4, pp. 548--564, November 1993.

No context found.

A. Orlitsky. Interactive communication of balanced distributions and of correlated files. SIAM Journal of Discrete Math, 6(4):548--564, 1993.

No context found.

A. Orlitsky. Interactive communication: Balanced distributions, correlated files, and average-case complexity. In IEEE Symposium on Foundations of Computer Science, pages 228--238, 1991.

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