D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", STOC, 1988, pp. 93--102.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the concept of oblivious routing was introduced. In this routing strategy the path of each packet is determined only by its source and destination position. It depends not on other packets. This makes oblivious routing simple and attractive and hence it was considered in several publications e.g. [1, 11, 14, 8, 15, 2, 13]. This simplicity has its costs in the running time. In [8] Kaklamanis, Krizanc, This work was supported in part by DFG Project Ku 658 8 3 and Tsantilas have shown that every oblivious permutation routing algorithm on a N node network with maximum node degree k needs at least W(N 2 =k) steps ....

KRIZANC, D., PELEG, D., AND UPFAL, E. A time-randomness tradeoff for oblivious routing. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing (Chicago, IL, May 1988), R. Cole, Ed., ACM Press, pp. 93--102.

....oblivious routing algorithms is interesting, since it allows one to design simple and hence practical algorithms. Furthermore it is of theoretical interest how fast it is possible to solve routing problems under such restrictions. Hence oblivious routing was considered in several publications e.g. [6, 5, 9]. It was shown that the simplicity of oblivious routing has its costs in the running time. In [5] Kaklamanis, Krizanc, and Tsantilas have shown that every oblivious k k routing algorithm on a network with N nodes and degree r needs at least W(k N=r) steps. One of the most studied parallel ....

D. Krizanc, D. Peleg, and E. Upfal. A time-randomness tradeoff for oblivious routing. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing, pages 93--102, 1988.

....used in computation is an important issue in many applications. Therefore, considerable effort has been devoted both to reduce the number of random bits used by probabilistic algorithms (see for instance [12] and to analyze the amount of randomness required in order to achieve a given performance [3, 4, 11, 14, 19]. Motivated by the fact that truly random bits are hard to obtain, it has also been recently investigated the possibility of using imperfect sources of randomness in randomized algorithms [20] Our approach is close in spirit to [2] in that we mainly concentrate on the rigourous quantification ....

D. Krizanc, D. Peleg, and E. Upfal, A Time--Randomness Tradeoff for Oblivious Routing, STOC 1988, pp. 93--102.

.... with the use of randomized protocols (see [17] Various techniques to minimize the amount of randomness needed were extensively studied in computer science (e.g. 36, 52, 10, 47, 54, 18, 32, 4, 46, 1, 50, 35, 37, 40, 33, 34] and tradeoffs between randomness and other resources were found (e.g. [14, 48, 38, 15, 21, 9, 8, 44, 7, 42, 40]) Security vs. Randomness. It is not hard to show that some randomness is essential to maintain security (if all parties are deterministic then the adversary can infer information on the parties inputs from their messages) We are interested in the amount of randomness required for carrying out ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", STOC, 1988, pp. 93--102.

....randomness complexity of such computations. Randomness is an important resource in computation. As a result, various methods for saving in randomness were studied [1, 6, 14, 19, 26, 28, 29, 30, 38, 39, 42, 44, 45, 47] In addition, the role of randomness in specific contexts was studied in, e.g. [41, 36, 4, 11, 8, 9]. One such case is the study of randomness in private multiparty computations [7, 12, 31, 34, 35, 22] In particular, in [7, 35, 31] the amount of randomness required for private computations of xor (the exclusive or function) was considered (this function was the subject of previous research in ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", Proc. of 20th STOC, 1988, pp. 93--102.

....of the model, and the fact that the complexity was naturally bounded by n 1. For any nonuniform model with a similar property, our proof asserts that one can use a small amount of randomness, i.e, the decision tree model, non uniform routing etc. Indeed the same idea was used in [1] [7]. 3. It is well known that for every pair of constants 0 ffl; ffl 0 if P 2 P com ffl (f) with C(P ) c, there exists a P 0 2 P com ffl 0 (f) whose complexity is O(c) for every (x; y) and all coin tosses. Using this, theorem 1.1 can be proved just by asserting property (1) property ....

Krizanc, D. Peleg, E. Upfal, A Time-Randomness Tradeoff for oblivious routing, Proc. 20th Annual ACM Symp. on theory of computing, 1988, 93-102.

....randomization is used to construct both more efficient and, not less significant, much simpler algorithms. Randomness as a resource was extensively studied in the last decade. One line of research was devoted to a quantitative study of the role of randomness in specific contexts, e.g. [RS89, KPU88, BGG90, CG90, BGS94, BSV94, KR94]; another direction was developing general purpose methods for saving random bits. These methods range over pseudo random Dept. of Computer Science, Technion. This research was supported in part by MANLAM Fund. e mail: eyalk cs.technion.ac.il) y Dept. of Computer Science, Tel Aviv ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing ", Proc. of 20th STOC, 1988, pp. 93--102.

.... [Cohen et al. 89, Impagliazzo et al. 89] to construct different kinds of small probability spaces (which sometimes even allow to eliminate the use of randomness) Koller et al. 93, Naor et al. 93] and to analyze the amount of randomness required in order to achieve a given performance [Krizanc et al. 88, Kushilevitz et al. 94] A secret sharing scheme is a method to share a secret s among a set P of participants in such a way that only qualified subsets of P, pooling together their information, can reconstruct the secret s; whereas, any other (non qualified) subset of P has no information on it. ....

Krizanc, D., Peleg, D., Upfal, E.: "A Time--Randomness Tradeoff for Oblivious Routing"; Proc. 20th Annual ACM Symposium on Theory of Computing (1988), 93--102.

.... by probabilistic algorithms [9, 15] to study weak random sources [28, 29] to construct different kind of small probability spaces (which sometimes even allow to eliminate the use of randomness) 17, 21] and 2 to analyze the amount of randomness required in order to achieve a given performance [18, 19]. Generating random bits by means of coin tosses or other physical processes is time consuming and expensive, so in practice it is common to use a pseudo random bit generator that expands a short random bit string into a much longer random looking bit string. Thus, a pseudo random bit generator ....

D. Krizanc, D. Peleg, and E. Upfal, A Time--Randomness Tradeoff for Oblivious Routing, in Proceedings of 20th Annual ACM Symposium on Theory of Computing, 1988, pp. 93--102.

.... [CD89] Various techniques to minimize the amount of randomness needed were extensively studied in computer science (e.g. AGHP90, BGG90, BM82, CG85, IZ89, KK94, KM93, KM94a, KM94b, KM96, KY76, N90, NN90, S92, Y82a, Z91] and tradeoffs between randomness and other resources were found (e.g. [BDPV95, BGS94, BSV94, CG90, CK93, CRS93, KM96, KOR96, KPU88, KR94, RS89]) Security vs. Randomness. It is not hard to show that, except for degenerate cases, some randomness is essential to maintain security (if all parties are deterministic then the adversary can infer information on the parties inputs from their messages) We are interested in the amount of ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", STOC, 1988, pp. 93--102.

....is the case t = 1. Randomness is an important resource in computation. As a result, various methods for saving in randomness were studied [1, 6, 14, 19, 25, 27, 28, 29, 36, 37, 40, 42, 43, 44] In addition, there was a quantitative study of the role of randomness in specific contexts, e.g. [39, 34, 4, 11, 8, 9]. One such case is the study of randomness in private multiparty computations [7, 12, 30, 32, 33, 22] In particular, in [7, 33, 30] the amount of randomness required for private computations of xor (the exclusive or function) was considered (this function was the subject of previous research in ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", Proc. of 20th STOC, 1988, pp. 93--102.

....[76] Valiant s routing algorithm on the binary hypercube requires O(N log N) bits of randomness. Ranade showed how to route on the hypercube in O(log N) time using only O(log 2 N) random bits [267] The effects of limited randomness and pseudorandomness on routing time were studied in [135, 243, 313]. Global Communications. Global communication schemes on hypercubes have been extensively considered. Broadcasting can be easily implemented, since the hypercube belongs to the class of broadcasting graphs, i.e. in a broadcasting graph, the number of nodes possessing the necessary information can ....

Peleg, D., and Upfal, E. A time randomness tradeoff for oblivious routing. SIAM J. Comput. 19 (2), 1990, pp. 256--266.

....first problem is strictly related to the security of the schemes, since the security of any system degrades as the amount of secret information increases. The problem of estimating the number of random bits necessary to implement randomized algorithms is receiving considerable interest (see [13] [17], for example) This is due to the fact that the amount of randomness needed by an algorithm is to be considered a computational resource, analogously to the amount of time and space needed. The quantitative study of the number of random bits needed by secret sharing schemes has been initiated in ....

....used in computation is an important issue in many applications. Therefore, considerable effort has been devoted both to reduce the number of random bits used by probabilistic algorithms (see for instance [13] and to analyze the amount of randomness required in order to achieve a given performance [17]. The Shannon entropy of the random source generating the random bits represents the most general and natural measure of randomness. In this section we define the dealer s randomness for secret sharing schemes with broadcast message. We present a lower bound on the dealer s randomness R(A) of any ....

D. Krizanc, D. Peleg, and E. Upfal, A Time--Randomness Tradeoff for Oblivious Routing, Proceedings of 20th Annual ACM Symposium on Theory of Computing, pp. 93--102, 1988.

.... [CG88, VV85, Z91] and constructions of different kinds of small probability spaces [NN90, AGHP90, S92, KM93, KM94, KK94] which sometimes even allow to eliminate the use of randomness) A different direction of research is a quantitative study of the role of randomness in specific contexts, e.g. [RS89, KPU88, BGG90, CG90, BGS94, BSV94]. In this work, we initiate a quantitative study of randomness in private computations. We mainly concentrate on the specific task of computing the xor of n input bits. However, most of our results extend to any boolean function. The task of computing xor was the subject of previous research due ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", Proc. of 20th STOC, 1988, pp. 93--102.

....in computation is an important issue in many applications. Therefore, considerable effort has been devoted both to reducing the number of random bits used by probabilistic algorithms (see for instance [21] and to analyzing the amount of randomness required in order to achieve a given performance [25]. The Shannon entropy of the random source generating the random bits represents the most general and natural measure of randomness. Indeed, Knuth and Yao [24] have shown that the Shannon entropy of a random variable is closely related to a more algorithmically oriented A preliminary version of ....

D. Krizanc, D. Peleg, and E. Upfal, A Time--Randomness Tradeoff for Oblivious Routing, Proceedings 20th ACM Symposium on Theory of Computing, 1988, pp. 93--102.

....used in computation is an important issue in many applications. Therefore, considerable effort has been devoted both to reduce the number of random bits used by probabilistic algorithms (see for instance [12] and to analyze the amount of randomness required in order to achieve a given performance [3, 4, 11, 14, 19]. Motivated by the fact that truly random bits are hard to obtain, it has also been recently investigated the possibility of using imperfect sources of randomness in randomized algorithms [20] Our approach is close in spirit to [2] in that we mainly concentrate on the rigourous quantification ....

D. Krizanc, D. Peleg, and E. Upfal, A Time--Randomness Tradeoff for Oblivious Routing, STOC 1988, pp. 93--102.

.... with the use of randomized protocols (see [16] Various techniques to minimize the amount of randomness needed were extensively studied in computer science (e.g. 35, 50, 10, 45, 52, 17, 31, 4, 44, 1, 48, 34, 36, 39, 32, 33] and tradeoffs between randomness and other resources were found (e.g. [13, 46, 37, 14, 20, 9, 8, 42, 7, 41, 39]) Security vs. Randomness. Clearly, some randomness is essential to maintain security (if all parties are deterministic then the adversary can infer information on the parties inputs from their messages) We are interested in the amount of randomness required for carrying out a t resilient ....

D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", STOC, 1988, pp. 93--102.

....(i.e. no error allowed, as opposed to our Monte Carlo model) in the two way, local coins model. In their setting, they show a tight tradeoff similar to the one presented in this paper 1 . Note that a quantitative study of randomness was carried out in the context of oblivious routing [KR,KPU], and for cashing algorithms [RS] Organization. In section 2 we define the models and the parameters to be discussed. Section 3 contains the lower bounds for the four models. In section 4 we present functions and protocols for these functions that demonstrate the tightness of the bounds. ....

Krizanc, D., D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", Proc. of 20th STOC, pp. 93-102, 1988.

....steps, so as to amortize the Omega Gammae 1 N) transfer time through the network. If log N extra randomizing stages are used, then t consecutive permutations can be routed optimally in time O(t log N ) with high probability [14] Can we achieve the same effect at less cost It was shown in [8] that fewer randomizing stages will not do; if less than (log N) 2 randomizing stages are used, then a worst case permutation requires Omega Gamma p N ) to be routed; t successive executions of that same worst case permutation will require Omega Gamma t p N) steps to be routed. ....

P. Peleg and E. Upfal, A time-randomness tradeoff for oblivious routing. SIAM J. on Computing, Vol. 19, 1990. pp. 256--266.

....problems for which the best known randomized algorithm performs substantially better than the best known deterministic algorithm. However, oblivious packet routing is one of a very few problems for which there is a proven gap between its randomized and deterministic complexity. Peleg and Upfal [35] have used this fact for a study of randomness as a resource. Their main result is am almost tight tradeoff between the amount of randomness given to an oblivious routing algorithm, and its performance. Theorem 5. Let e 3 log N T p N=2d, and assume that the only source of randomness ....

....a randomized oblivious algorithm does not perform better than a deterministic oblivious algorithm. Any additional random bit, above the first 1 2 log N bits, improves the run time by a constant factor, until the run time reaches the O(logN ) diameter bound. Similar results have been given in [35] for a general random source, measuring randomness by the entropy of the source. 3.4 Information Dispersal Information Dispersal is an elegant probabilistic routing technique that achieves near optimal routing time, uses bounded buffers, and has high fault tolerance properties. This technique ....

D. Peleg and E. Upfal. Time-randomness trade-off for oblivious routing. SIAM Journal on Computing, 19:256--266, 1990.

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D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", STOC, 1988, pp. 93--102.

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D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", Proc. of 20th STOC, 1988, pp. 93--102. 12

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D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing", Proc. of 20th STOC, 1988, pp. 93--102.

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D. Krizanc, D. Peleg, and E. Upfal, "A Time-Randomness Tradeoff for Oblivious Routing ", Proc. of 20th STOC, 1988, pp. 93--102.

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D. Peleg and E. Upfal. A time-randomness trade-off for oblivious routing. SIAM Journal of Computing, 19(2):256--266, April 1990.

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