In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more "on-line" than earlier similar methods, tak...
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In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more "on-line" than earlier similar methods, takes expected time O(n\log n) and space O(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing Voronoi diagrams obviates the need for building a separate point-location structure for nearest-neighbor queries.
Two new heuristics are presented for inferring a small size Boolean function from complete and incomplete examples in polynomial time. These examples are vectors defined in {1, 0}(n) for the complete case, or in {1,0,...
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Two new heuristics are presented for inferring a small size Boolean function from complete and incomplete examples in polynomial time. These examples are vectors defined in {1, 0}(n) for the complete case, or in {1,0, *}(n) for the incomplete case (where n is the number of binary attributes or atoms and "*" indicates unknown value). Each example is either positive or negative, if it must be accepted or rejected by the target function, respectively. For the incomplete case, however, some examples may be unclassifiable. Moreover, computational results indicate that the proposed heuristics may also be effective in solving very large problems with thousands of examples.
Model structure selection (MSS) is a critical problem in the nonlinear identification field. In the framework of polynomial nonlinear autoregressive [moving average] models with exogenous input variables, it is formul...
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Model structure selection (MSS) is a critical problem in the nonlinear identification field. In the framework of polynomial nonlinear autoregressive [moving average] models with exogenous input variables, it is formulated as the combinatorial problem of finding the subset of regressors that yields optimal model accuracy. Increasing the set of potential model terms improves the flexibility of the model but results in a computational overload and may even jeopardize the ability of the MSS algorithm to find the optimal model. In this work, a distributed optimization scheme is developed to tackle the MSS task for large-sized candidate regressor sets. The regressor set is split among a group of independent processors, and each of them executes an MSS routine on its local subset. Then, the processors exchange information regarding the selected models, and the corresponding regressors are distributed among all the units for a new MSS round. The procedure is repeated until convergence of all processors to the same solution. Besides a drastic reduction in the computational time, thanks to the inherent parallelizability of the algorithm execution, the proposed distributed optimization scheme can also be beneficial in terms of model accuracy, due to a more efficient exploration of the search space.
A new randomized Byzantine agreement algorithm is introduced. This algorithm functions in a synchronous system of n processors, at most t of which can fail. The algorithm reaches agreement in given expected rounds a...
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A new randomized Byzantine agreement algorithm is introduced. This algorithm functions in a synchronous system of n processors, at most t of which can fail. The algorithm reaches agreement in given expected rounds and given expected message bits independent of the distribution of processor failures. This performance is improved to a constant expected number of rounds and message bits if the distribution of processor failures is assumed to be uniform. In either case, the algorithm improves on the known lower limit on rounds for deterministic algorithms. Other benefits of the algorithm include: 1. It requires no cryptographic methods. 2. The amount of local computation is small. 3. The expected number of random bits used per processor is only one. It is argued that, in many practical applications of Byzantine agreement, the randomized algorithm presented here achieves superior performance.
In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R(f). The certificate complexity C(f) is such a complexity measure for the zero-error...
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In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R(f). The certificate complexity C(f) is such a complexity measure for the zero-error randomized query complexity R0(f): C(f) = R0(f) = C(f)2. In the first part of the paper we introduce a new complexity measure, expectational certificate complexity EC(f), which is also a quadratically tight bound on R0(f): EC(f) = R0(f) = O(EC(f)2). For R(f), we prove that EC2/3 = R(f). We then prove that EC(f) = C(f) = EC(f)2 and show that there is a quadratic separation between the two, thus EC(f) gives a tighter upper bound for R0(f). The measure is also related to the fractional certificate complexity FC(f) as follows: FC(f) = EC(f) = O(FC(f)3/2). This also connects to an open question by Aaronson whether FC(f) is a quadratically tight bound for R0(f), as EC(f) is in fact a relaxation of FC(f). In the second part of the work, we investigate whether the corruption bound corr (f) quadratically approximates R(f). By Yao's theorem, it is enough to prove that the square of the corruption bound upper bounds the distributed query complexity D mu (f) for all input distributions mu. Here, we show that this statement holds for input distributions in which the various bits of the input are distributed independently. This is a natural and interesting subclass of distributions, and is also in the spirit of the input distributions studied in communication complexity in which the inputs to the two communicating parties are statistically independent. Our result also improves upon a result of Harsha et al. (2016), who proved a similar weaker statement. We also note that a similar statement in the communication complexity is open.
We present the first explicit, and currently simplest, randomized algorithm for two-process wait-free test-and-set. It is implemented with two 4-valued single writer single reader atomic variables. A test-and-set take...
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We present the first explicit, and currently simplest, randomized algorithm for two-process wait-free test-and-set. It is implemented with two 4-valued single writer single reader atomic variables. A test-and-set takes at most 11 expected elementary steps, while a reset takes exactly 1 elementary step. Based on a finite-state analysis, the proofs of correctness and expected length are compressed into one table.
In many fault detection problems, we want to identify all defective items from a set of n items using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells w...
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In many fault detection problems, we want to identify all defective items from a set of n items using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number d of defective items is often unknown in advance. In this paper, we propose a randomized group testing procedure RGT for the scenario where the number d of defectives is unknown in advance, and prove that RGT is competitive. By incorporating numerical results, we obtain improved upper bounds on the expected number of tests performed by RGT, for . In particular, for and the special case where n is a power of 2, we obtain an upper bound of with on the expected number of tests performed by RGT, which is better than the currently best upper bound in Cheng et al. (INFORMS J Comput 26(4):677-689, 2014). We conjecture that the above improved upper bounds based on numerical results from actually hold for all d >= 1.
We present a lower bound of 1 + e(-1/2) approximate to 1.6065 on the competitive ratio of randomized algorithms for the weighted 2-cache problem, which is a special case of the 2-server problem. This improves the Prev...
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We present a lower bound of 1 + e(-1/2) approximate to 1.6065 on the competitive ratio of randomized algorithms for the weighted 2-cache problem, which is a special case of the 2-server problem. This improves the Previously best known lower bound of e/(e-1) approximate to 1.582 for both problems. (C) 1997 Elsevier Science B.V.
We deal with quantum and randomized algorithms for approximating a class of linear continuous functionals. The functionals are defined on a Holder space of functions f of d variables with r continuous partial derivati...
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We deal with quantum and randomized algorithms for approximating a class of linear continuous functionals. The functionals are defined on a Holder space of functions f of d variables with r continuous partial derivatives, the rth derivative being a Holder function with exponent rho. For a certain class of such linear problems (which includes the integration problem), we define algorithms based on partitioning the domain of f into a large number of small subdomains, and making use of the well-known quantum or randomized algorithms for summation of real numbers. For N information evaluations (quantum queries in the quantum setting), we show upper bounds on the error of order N (-(gamma+1)) in the quantum setting, and N (-(gamma+1/2)) in the randomized setting, where gamma = (r + rho)/d is the regularity parameter. Hence, we obtain for a wider class of linear problems the same upper bounds as those known for the integration problem. We give examples of functionals satisfying the assumptions, among which we discuss functionals defined on the solution of Fredholm integral equations of the second kind, with complete information about the kernel. We also provide lower bounds, showing in some cases sharpness of the obtained results, and compare the power of quantum, randomized and deterministic algorithms for the exemplary problems.
A randomized on-line algorithm is given for competitiveness less than 1901 against the previously best known competitiveness of IN uses a new approach and defines a potential in the 2-server problem on the line, with ...
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A randomized on-line algorithm is given for competitiveness less than 1901 against the previously best known competitiveness of IN uses a new approach and defines a potential in the 2-server problem on the line, with oblivious adversary. This improves the 155/78 approximate to 1.987 for the problem. The algorithm terms of isolation indices from T-theory. (C) 2015 Elsevier B.V. All rights reserved.
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