U. Feige, D. Peleg, P. Raghavan, E. Upfal, "Computing with unreliable information," Proc. 22nd ACM STOC, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....n players using unreliable comparisons was addressed in [RGL] where Ravikumar, Ganesan and Lakshmanan assume that the total number of erroneous outcomes is less than some absolute upper bound e. They show that (e 1)n Gamma 1 comparisons are necessary and sufficient to find the best player. In [FPRU], Feige, Peleg, Raghavan and Upfal choose a probabilistic model, assuming that each comparison has a fixed probability p of being erroneous, and that successive comparisons are independent. The goal is then to select the best player with probability at least 1 Gamma Delta, for some fixed ....

U. Feige, D. Peleg, P. Raghavan and E. Upfal. "Computing with Unreliable Information". In Symposium on Theory of Computing, 1990, 128137.

....of the noisy computation by Boolean circuits of any nonconstant symmetric function of n variables is 24 n) 3 We note that there is a di erence between the redundancies of noisy computations by circuits and by decision trees. A similar model of noisy computation is considered by Feige et al. [4] for Boolean decision trees. The nodes of the tree are allowed to be independently faulty with some probability, and the result of the computation has to be correct with at least a xed probability for every input. Feige et al. 4] give bounds for the depth of noisy decision trees computing ....

....A similar model of noisy computation is considered by Feige et al. 4] for Boolean decision trees. The nodes of the tree are allowed to be independently faulty with some probability, and the result of the computation has to be correct with at least a xed probability for every input. Feige et al. [4] give bounds for the depth of noisy decision trees computing symmetric functions. These bounds show that some nonconstant symmetric functions have constant redundancy of noisy computation by decision trees. Corollary 2.7 There exist Boolean functions of n variables with constant redundancy of ....

U. Feige, D. Peleg, P. Raghavan and E. Upfal, \Computing with unreliable information," In Proc. of 22th ACM Symposium on the Theory of Computing, 1990, pp. 128-137.

....model, like ours, has a mixing time of O(N ) for p 1 2. Our Markov chains are closely related to the bubble sort algorithm. The chain d (N, 1) CA d (N, 0) is performing a randomized version of the bubble sort algorithm which converges to (1, 2, N) N, N 1, 1) In [8] the authors introduce a model of computation where each comparison operation has probability p 1 2 of returning the true result and probability 1 p of returning a false result independently of other comparisons. The chain p) CA d (N, p) is performing the randomized version of bubble ....

U. Feige, D. Peleg, P. Raghavan and E. Upfal (1990), Computing with unreliable information, STOC 90, 128-137.

....and thus require only O(1) bits of communication. We are now in the situation of searching for a number, i sig , in the range 1: n using queries of the form i sig i , where each answer may be incorrect with a small constant probability. This situation has been studied in the literature, and [FPRU90] show how it can be done, with probability of error ffl, using O(log n log ffl ) queries. 2 Remark: The improved protocol is not really needed for any of the applications, without it we would simply loose another log n factor in all our lower bounds. Remark: The upper bound is in fact ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the 22nd STOC, pages 128--137, 1990.

....game and h4; 0i almost opportunistic in an atomic game. 1.7.4 Searching in the Presence of Errors The problem of searching interactively under the assumption that some answers may be erroneous is well investigated. It was first introduced by Ulam [69] and addressed by numerous researchers [61, 60, 22, 30, 24, 6, 66, 67, 5]. Most of these papers model it by a multistage game. The searcher is commonly called Paul and his adversary Carole. The 48 problem most of these papers address is searching for a single value in a finite domain. In Rivest et al. 61] and Pelc [60] the authors consider finding the ffl vicinity of ....

U. Feige, D. Peleg, P. Raghavan, and Upfal E. Computing with unreliable information. In Proceedings of the Twenty Second Annual ACM Symposium on Theory of Computing, pages 128--137. ACM Press, 1990.

....n) O(n lg ) Figure 7.1: Bounds for searching in the bounded domain with linearly bounded errors. Here n is a bound on the number being sought. improved the bound to O(lg n lg lg n) questions using a somewhat complicated analysis. Finally, using standard Chernoff bound techniques, Feige et al. [12] showed that O(lg n) questions are sufficient for any p 1 2. Our contribution here is a formal reduction from the problem of searching in the probabilistic error model to that of searching in the linearly bounded error model. To state this result informally, we show that an algorithm for ....

....2 [lglgn llg7 O( lglgn] 2) lglgnl ( lglgnl 1) 1 2 We thus bound the unknown number n by at most n using O( lg lg n] comparison) questions. We can now simply apply the bounded searching techniques for membership questions described in previous section or the bounds of Feige et al. [12] for comparison questions. We can thus obtain the correct answer (with high probability) in an additional O(lg n 2) O(lg n) comparison or membership questions. Thus, we can conclude the following theorem: Theorem 30 The problem of searching for an unknown element n in the unbounded domain of ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the Twenty-Second Annual A CM Symposium on Theory of Computing, pages 128-137, 1990.

....O(lgn) O(n Figure 7.1: Bounds for searching in the bounded domain with linearly bounded errors. Here n is a bound on the number being sought. improved the bound to O(lg n lg lg n) questions using a somewhat complicated analysis. Finally, using standard Chernoff bound techniques, Feige et al. [12] showed that O(lg n) questions are sufficient for any p 1=2. Our contribution here is a formal reduction from the problem of searching in the probabilistic error model to that of searching in the linearly bounded error model. To state this result informally, we show that an algorithm for ....

....lg ne lg dlg lg ne(dlg lg ne 1) O( lg lg n] We thus bound the unknown number n by at most n using O( lg lg n] comparison) questions. We can now simply apply the bounded searching techniques for membership questions described in previous section or the bounds of Feige et al. [12] for comparison questions. We can thus obtain the correct answer (with high probability) in an additional O(lg n ) O(lg n) comparison or membership questions. Thus, we can conclude the following theorem: Theorem 30 The problem of searching for an unknown element n in the unbounded domain of ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, pages 128--137, 1990.

....graph [2, 7, 16] In neither case do the nodes contain information of the type considered here that might direct the search. In the restaurant analogy, there are no informed policeman. We feel our work is closer in spirit to that of computing with uncertainty or with noisy computing elements [9, 10, 13, 17]. An important distinction between the two situations is that noisy computing elements are sometimes correct and sometimes in error while in our case a database entry is correct or in error for the run of the algorithm, i.e. a policeman always reports the same information for the same query. In ....

U. Fiege, D. Peleg, P. Raghavan and E. Upfal, "Computing with unreliable information," STOC 90, 128-137.

....on the techniques of AKS. Throughout this section, let A = P;I; ae; n Gammac ) and B = P;II; ae; n Gammac ) where ae 1 and c denotes an arbitrary positive constant. 5. 1 Insertion A number of authors have studied the problem of binary search in a faulty environment (see, for example, [5, 7, 13]) However, none of these results seem to extend to the faulty comparator circuit model. The main result of this section is summarized by the following theorem. Theorem 3 For all m n and some constant fl, 0 fl 1, we have jInsert(m; m fl ; A)j = O(log n) We prove the preceding theorem by ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 128--137, May 1990.

....log n) comparators are needed to construct a fault tolerant sorting or merging circuit, but no proof of this conjecture has yet been discovered. Since Yao and Yao, many researchers have studied fault tolerant circuits, networks, and algorithms for sorting related problems in various models. See [4, 6, 7, 12, 13, 18, 19, 20]. Despite all of these efforts, the O(log n) gap between the trivial upper and lower bounds has remained open for Yao and Yao s question for both sorting and merging. One approach to narrowing the O(log n) gap was investigated by Leighton, Ma, and Plaxton [13] who constructed an O(n log n log ....

....1 Gamma 1 n even if an answer to any comparison query is incorrect with probability upper bounded by a constant strictly less than 1 2 . Note that when the fault probability is equal to 1 2 , we cannot obtain any useful information from a comparison. Feige, Peleg, Raghavan, and Upfal [7] designed a randomized fault tolerant sorting algorithm that uses O(log n) expected time on an O(n) processor CREW PRAM. They left open the question of whether or not there is a deterministic fault tolerant sorting algorithm that runs in o(log 2 n) steps on O(n) processors. In this paper, we ....

[Article contains additional citation context not shown here]

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the 22nd Annual ACM Symposium on the Theory of Computing, pages 128--137, May 1990.

.... computed by a noisy static decision tree with O(n log n) queries (with 2 log(n=ffi) ffi log Gamma 1=4 (1 Gamma ) Delta = O(log n) queries, it is possible to determine a single argument with error probability at most ffi=n) Noisy dynamic decision trees were considered by Feige et al. [F1,F2], who showed that there are noisy dynamic decision trees that reliably compute the disjunction or conjunction of n arguments with O(n) queries. Since we have seen that noisy static decision trees 2 require Omega Gamma n log n) queries, this exhibits a clear separation between the two models. ....

....trees that reliably compute the disjunction or conjunction of n arguments with O(n) queries. Since we have seen that noisy static decision trees 2 require Omega Gamma n log n) queries, this exhibits a clear separation between the two models. For noisy dynamic decision trees, Feige et al. [F1,F2] showed that Omega Gamma n log n) queries are needed to compute the parity or majority of n arguments, and Reischuk and Schmeltz [R] showed that Omega Gamma n log n) queries are needed for almost all Boolean functions of n arguments. This last result contrasts with results of Muller [M] and ....

[Article contains additional citation context not shown here]

U. Feige, D. Peleg, P. Raghavan and E. Upfal, "Computing with Unreliable Information ", Proc. ACM Symp. on Theory of Computing, 22 (1990) 128--137.

....queries are answered incorrectly. In addition to the aforementioned previous work, sorting and searching with a faulty comparison oracle has been studied under at least two other assumptions about the generation of the faults, including that they are generated independently at random [Pel89, FPRU90] and that there is a constant r such that for each i, at most ir of the first i comparisons are answered incorrectly [Pel89, AD91] 2 Approximating P d i=0 i m i j In this section, we state and, for completeness, prove, a useful approximation to P d i=0 Gamma m i Delta . The following ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. Proceedings of the 22nd ACM Symposium on the Theory of Computation, 1990.

....the noisy computation by Boolean circuits of any nonconstant symmetric function of n variables is Omega Gamma 38 n) We note that there is a difference between the redundancy of noisy computation by circuits and by decision trees. A similar model of noisy computation is considered by Feige et al. [33] for Boolean decision trees. The nodes of the tree are allowed to be independently faulty with some probability, and the result of the computation has to be correct with at least a fixed probability for every input. Feige et 16 al. 33] give bounds for the depth of noisy decision trees computing ....

....model of noisy computation is considered by Feige et al. 33] for Boolean decision trees. The nodes of the tree are allowed to be independently faulty with some probability, and the result of the computation has to be correct with at least a fixed probability for every input. Feige et 16 al. [33] give bounds for the depth of noisy decision trees computing symmetric functions. These bounds show that some nonconstant symmetric functions have constant redundancy of noisy computation by decision trees. Corollary 2.1.7 There exist Boolean functions of n variables with constant redundancy of ....

U. Feige, D. Peleg, P. Raghavan and E. Upfal, "Computing with unreliable information ", In Proc. of "22nd ACM Symposium on the Theory of Computing", 1990, pp. 128-137.

....all the questions before answering, the threshold drops to 1 4 . Author s net address: spencer cs.nyu.edu y Author s net address: pw bellcore.com The Game The problem of computing from unreliable information has attracted much interest in recent years. A typical model (see, for example, FPRU90] involves an oracle which, each time it is queried, responds falsely independently with probability some fixed p. Then the object is to design an algorithm which performs the required task correctly with probability arbitrarily close to 1, and with complexity not greatly exceeding that needed ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Symposium on Theory of Computing, pages 128--137, 1990.

....computing the sum of at most d products of two elements. Remark: Some improvements of the above implementation are possible. For example, note that the value of M was chosen so as to guarantee that with constant probability no mistake is made throughout the binary search. Using results of [16], a binary search can still be made in O(log d) steps even if there is a constant probability of error at each step. This allows choosing M which is smaller by a O(log d) factor and get the corresponding improvement in the size of S and the time required to construct it. 3 Approximate Nearest ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proc. of 22nd STOC, pp. 128--137, 1990.

....the main issues that distinguish DNA computers from conventional computers. Not surprisingly, it also distinguishes the problem of making DNA computations error resilient from the issue of computing with unreliable operations on conventional computers, that has been the focus of much research (cf. [8, 9, 10, 11, 14, 15, 16, 17, 18]) 1.2 Our results In this paper we provide a method for making computations error resilient without a big sacrifice in their running time, and derive lower bounds on the cost of such methods. We start with the problem that is at the core of all error resilient DNA computations: simulate a ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the 22nd ACM Symposium on Theory of Computing, pages 128--137, 1990.

....it turns out that overcoming such a noise with only a constant increase in the cost may be non trivial and in some cases impossible. Such a noise model was studied in the context of circuits with noisy gates (e.g. N56, DO77a, DO77b, Pip85, G al91, RS91] decision trees with noisy nodes (e.g. [FPRU90, RS91, EP96]) communication complexity ( Sch92, Sch93, RS94] and others (e.g. Tay68, Kuz73, G ac86, Spi96] In this paper we consider noisy radio (broadcast) networks. The main feature of radio networks is that when a processor sends a message all its neighbors receive it. There has been a considerable ....

U. Feige, D. Peleg, P. Raghavan, and E. Upfal, "Computing with Unreliable Information", Proc. of 22nd STOC, pp. 128--137, 1990.

....n players using unreliable comparisons was addressed in [RGL] where Ravikumar, Ganesan and Lakshmanan assume that the total number of erroneous outcomes is less than some absolute upper bound e. They show that (e 1)n Gamma 1 comparisons are necessary and sufficient to find the best player. In [FPRU], Feige, Peleg, Raghavan and Upfal choose a probabilistic model, assuming that each comparison has a fixed probability p of being erroneous, and that successive comparisons are independent. The goal is then to select the best player with probability at least 1 Gamma Delta, for some fixed ....

U. Feige, D. Peleg, P. Raghavan and E. Upfal. "Computing with Unreliable Information". In Symposium on Theory of Computing, 1990, 128137.

.... elimination tournament on the set of points; the tournament returns an approximate nearest neighbor with high probability using a linear number of comparisons. We note that the analysis of tournaments with unreliable comparisons has been the subject of a number of previous papers (see e.g. [21, 1] and the references therein) however, the actual models considered in these papers are technically fairly distinct from the constraints imposed by our application here. 2 Some Geometric Lemmas In this section, we prove some of the geometric lemmas required for the analysis of our algorithms. It ....

U. Feige, D. Peleg, P. Raghavan, E. Upfal, "Computing with unreliable information," Proc. 22nd ACM STOC, 1990.

No context found.

U. Feige, D. Peleg, P. Raghavan, E. Upfal, "Computing with unreliable information," Proc. 22nd ACM STOC, 1990.

No context found.

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proc. of 22nd STOC, pp. 128--137, 1990.

No context found.

U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Computing with unreliable information. In Proceedings of the 22nd ACM Symposium on Theory of Computing, pages 128--137, 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC