ABI]Alon, N., L. Babai, A. Itai, A fast and simple randomized parallel algorithm for the [ maximal independent set problem, J. of Algorithms, 7(1986), pp. 567-583.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the same sparsi cation techniques of the preceding sections to augment I to a connected dominating set of size at most 3 jI j, which gives (essentially) a 12approximation. It is well known that an MIS can be computed in O(log n) communication rounds in our distributed model using randomization [1, 11]. 5 Open Problems and Summary of results It would be nice to develop a more direct and computationally simpler method to obtain connected dominating sets with good stretch properties. One way to achieve this would be to solve the following problem. Let G = A; B; E) be a bipartite network. A ....

N. Alon, L. Babai, and A. Itai. A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem. J. Algorithms, 7:567-583, 1986.

....To get our PRF under the sf DDH assumption (i.e. in groups were regular DDH might be false) it sufficing to construct a 4 wise indepepndent encoding C . Naturally, the goal is to make L as close to as possible. Such encodings come up quite often in the theory of derandomization (see [ABI86, AS00] and are closely related to coding theory. In our case, the well known construction is very simple and efficient, so we present it in a self contained manner. Let us now view any element of x 2 f0; 1g as an element of the field GF (2 ) which can be represented as an ....

Noga Alon, Laszlo Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7:567--583, 1986.

....Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1 Introduction During the last years there is a growing interest in techniques for removing randomness from parallel (and sequential) algorithms. These techniques were originated by [7, 8] and generalized in [1, 2, 4, 6, 9, 10, 11]. The approach usually followed can be summarized as follows: The random variables which are considered are defined over a smaller probability space, specially designed, containing only a polynomial number of sample points. In that space, the random variables are only k wise independent (for ....

N. Alon, L. Babai and A. Itai, A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem, Journal of Algorithms 7 (1986) 567-583.

....and other randomized rounding algorithms. Randomized rounding of linear programs and the method of pessimistic estimators has since been quite popular in the design of approximation algorithms (see [MNR95] Returning to the context of parallel algorithmic derandomization, Alon, Babai, and Itai [ABI86] gave optimal constructions of k wise independent binary random variables. However, it was soon realized that O(1) wise independent binary random variable constructions were inadequate to derandomize many parallel algorithms; n random variables that are roughly O(log n) wise independent seemed to ....

N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7:567--583, 1986.

....are fairly tight. In fact, the above inequality automatically gives a logspace algorithm to obtain a 2 approximation to K(oe) since one can easily compute F (oe) when oe appears in a stream. We assume that the permutation is presented in its inverted form, i.e. in the form of an array oe[1]; oe[n] such that the i th entry of the array oe[i] u if and only if oe(u) i. We use square brackets or parentheses to indicate the semantics for the use of oe. A list L = L[1] L[n] drawn from a universe [m] is a sequence of n ordered elements such that for each i, L[i] 2 ....

....a stream. We assume that the permutation is presented in its inverted form, i.e. in the form of an array oe[1] oe[n] such that the i th entry of the array oe[i] u if and only if oe(u) i. We use square brackets or parentheses to indicate the semantics for the use of oe. A list L = L[1]; L[n] drawn from a universe [m] is a sequence of n ordered elements such that for each i, L[i] 2 [m] Though a list is not necessarily a permutation, the notion of inversions in a list can still be defined. Let K(L) denote the number of pairs hi; ji such that i j and L[i] L[j] Given ....

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4):567--583, 1986.

....a subset S of V that does not contain any edge. S is a maximal independent set (MIS) if no proper superset of S is an IS. It is easy to find an MIS sequentially, but efficient parallel algorithms appear much harder. There has been much work on finding MISs in parallel in (hyper)graphs (see, e.g. [1, 4, 7, 9, 17, 15, 16, 18, 21]) Since an MIS can be much smaller than a maximum independent set (as in the case of a star graph) it is also of much interest to find ISs that have a guaranteed size. What is known in this context Recall that given a hypergraph H = V; E) the degree of a vertex is the number of edges that it ....

....graph families for which ff 2 (G) Theta(n) and n 2 = 2m n) is just Theta(1) see item (i) in Section 1.2. Recently, the second author developed an NC algorithm that finds an IS of size (1 Gamma o(1) Delta ff 2 (G) where the o(1) term goes to zero as n 1 [24] Alon, Babai and Itai [1] studied the MIS problem on hypergraphs: they gave an NC algorithm that finds an IS of size c(n k =m) 1= k Gamma1) 0 c 1, in k uniform hypergraphs with k 2 being any constant. The work of Karger and Koller [13] generalized this to arbitrary k. 1.2 Main Results We give an RNC algorithm ....

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N. Alon, L. Babai and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms, 7, pp. 567--583, 1986.

....random variables rather than totally independent ones. The generation of k wise independent and approximately k wise independent random variables has been well studied [Jof74, CG89, NN93, EGL 98, CRS00] Early applications of k wise independence in derandomization can be found in [KW85, Lub86, ABI86, Lub93, BR91] Very recently Klivans and Spielman [KS01] gave a randomness ecient method for testing if a polynomial is identically zero. In all of these algorithms a reduction in randomness is traded for suboptimal performance. 1.1 Our Results In this paper we address the issue of reducing ....

N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algor., 7:567-583, 1986.

....a specific class has a good bound on the expected size of the largest bucket is to build a class specifically designed to have such good property. One immediate such result is obtained by looking at the class of d degree polynomials over finite fields, where d = c log n= log log n (see, e.g. [ABI86]. It is easy to see that this class maps each d elements of the domain independently to the range, and thus, the bound that applies to the class of all functions also applies to this class. We can combine this with the following well known construction, which is usually called collapsing the ....

N. Alon, L. Babai and A. Itai, A fast and simple randomized parallel algorithm for the maximal independent set problem. J. 20 Algorithms 7 (1986) 567--583.

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ABI]Alon, N., L. Babai, A. Itai, A fast and simple randomized parallel algorithm for the [ maximal independent set problem, J. of Algorithms, 7(1986), pp. 567-583.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7:567--583, 1986.

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N. Alon, L. Babai and A. Itai, A fast and simple randomized parallel algorithm for the maximal independent set problem, J. Algorithms, vol. 7(4), 1986, pp. 567-583.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4):567-- 583, Dec. 1986.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4):567--583, 1986.

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. N. Alon, L. Babai, A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms 7, 567-583(1986).

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N. Alon, L. Babai, A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms 7, 567-583(1986).

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N. Alon, L. Babai, A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms 7, 567-583(1986).

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N. Alon, L. Babai and A. Itai, A fast and simple randomized parallel algorithm for the maximal independent set problem, Journal of Algorithms 7 (1986), pp. 567--583.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7:567--583, 1986.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7:567--583, 1986.

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N. Alon, L. Babai, and A. Itai, "A fast and simple randomized parallel algorithm for the maximal independent Journal of Algorithms, 7 (1986) 567--583.

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Noga Alon, Laszlo Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4):567--583, 1986.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7 (1986), pp. 567--583.

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N Alon, L. Babai, A. Itai, \A fast and simple randomized parallel algorithm for the Maximal Independent Set Problem", Journal of Algorithms, Vol. 7, 1986, pp. 567-583.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7:567--583, 1986.

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N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7:567--583, 1986.

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