Following the recent independent proofs of Immerman [SIAM J. Comput., 17 (1988), pp. 935–938] and Szelepcsenyi [Bull. European Assoc. Theoret. Comput. Sci., 33 (1987), pp. 96–100] that nondeterministic space-bounded...
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Binary templates are optimally encoded in a reduced dimension by a proposed class of linear maps that preserves the local neighbourhood and a prescribed minimum distance between the prototypes to a workable extent. Th...
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Binary templates are optimally encoded in a reduced dimension by a proposed class of linear maps that preserves the local neighbourhood and a prescribed minimum distance between the prototypes to a workable extent. This in effect generates a nearness criterion suitable for template matching with a level of error correcting capability in the reduced space while requiring only a fraction of memory storage space and boolean operations that would have been required otherwise. Characters and symbols may now be designed with reference to separation and shape but with a comparative freedom from the constraint of dimension, while a volume of such data can be transmitted with the speed and bandwidth of the encoded data. Some of the principal problems associated with template matching are thus overcome. Here all the necessary operations are performed in the finite field GF(2) and the methodology developed can be implemented in a microcomputer with improved system performance and economy.
The principal shortcoming of simulated annealing (SA) is that it takes too much computer time. We present a few “swindling” ideas for speeding up SA by simulating its action on a problem. The increase in speed is at...
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The authors consider the problem of packing n items, which are drawn according to a probability distribution whose density function is triangular in shape, into bins of unit capacity. For triangles which represent den...
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The authors consider the problem of packing n items, which are drawn according to a probability distribution whose density function is triangular in shape, into bins of unit capacity. For triangles which represent density functions whose expectation is 1/p for p = 3, 4, 5,..., they give a packing strategy for which the ratio of the number of bins used in the packing to the expected total size of the items asymptotically approaches 1.
Boolean circuits of polynomial size and polylogarithmic depth are given for computing the Hermite and Smith normal forms of polynomial matrices over finite fields and the field of rational numbers. The circuits for th...
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Boolean circuits of polynomial size and polylogarithmic depth are given for computing the Hermite and Smith normal forms of polynomial matrices over finite fields and the field of rational numbers. The circuits for the Smith normal form computation are probabilistic ones and also determine very efficient sequential algorithms. Furthermore, we give a polynomial-time deterministic sequential algorithm for the Smith normal form over the rationals. The Smith normal form algorithms are applied to the rational canonical form of matrices over finite fields and the field of rational numbers.
The subset sum problem, when formulated as a decision problem (SS), is NP-complete, and the difficulty of solving it is the base of public key cryptosystems. It is demonstrated that each A-bounded subset sum problem ...
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The subset sum problem, when formulated as a decision problem (SS), is NP-complete, and the difficulty of solving it is the base of public key cryptosystems. It is demonstrated that each A-bounded subset sum problem SS(A) is nearly everywhere randomly decidable using an O(n) greedy algorithm. This theorem follows using a randomized version of the greedy algorithm, which is modeled as a Markov process with discrete time steps and discrete state space. A gap distribution is found that is identical to that found by d'Atri and Puech (1982) in their analysis of an algorithm similar to the algorithm GREEDYMSS presented. Further consideration is given to another randomized version of GREEDYMSS; however, there is no known analogous result about d'Atri and Puech's algorithm.
Chaitin and Schwartz [4] have proved that Solovay and Strassen [12], Miller [9], and Rabin [10] probabilistic algorithms for testing primality are error‐free in case the input sequence of coin tosses has maximal info...
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Chaitin and Schwartz [4] have proved that Solovay and Strassen [12], Miller [9], and Rabin [10] probabilistic algorithms for testing primality are error‐free in case the input sequence of coin tosses has maximal information *** this paper we shall describe conditions under which a probabilistic algorithm gives the correct output. We shall work with algorithms having the ability to make “random” decisions not necessarily binary (Zimand [13]). We shall prove that if a probabilistic algorithm is sufficiently “correct”, then it is error‐free on all sufficiently long inputs which are random in Kolmogorov and Martin-Löfs sense. Our result, as well as Chaitin and Schwartz's one, is only of theoretical interest, since the set of all random strings is immune (Calude and Chitescu [2]).
A family of balanced communication schemes for connecting N processors with only a constant number of lines entering or leaving each processor is defined. It is proved that this network topology enables a fully distri...
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A family of balanced communication schemes for connecting N processors with only a constant number of lines entering or leaving each processor is defined. It is proved that this network topology enables a fully distributed probabilistic algorithm to execute a variety of communication requests efficiently. In particular it enables implementation of an arbitrary permutation, that is, a set of N packets initially located in distinct processors and destined for distinct destinations in O(log//2N) steps. Similar results are proved for randomly generated communication requests. These results suggest an efficient solution to a fundamental problem in the design of parallel computers.
This review presents a probabilistic algorithm which computes the vertex connectivity of an undirected graph G=(V,E) in expected time Omicron ((-log epsilon) times the absolute value of V to the 31/2 power times the a...
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This review presents a probabilistic algorithm which computes the vertex connectivity of an undirected graph G=(V,E) in expected time Omicron ((-log epsilon) times the absolute value of V to the 31/2 power times the absolute value of E) with error probability at most epsilon provided that the absolute value of E is less than or equal to 11/2d times the absolute value of V squared for some universal constant d less than 1.
This paper presents an algorithm for the traveling salesman problem in k-dimensional Euclidean space. For n points independently uniformly distributed in a set $\mathbb{E}$, we show that, for any choice of a function ...
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This paper presents an algorithm for the traveling salesman problem in k-dimensional Euclidean space. For n points independently uniformly distributed in a set $\mathbb{E}$, we show that, for any choice of a function $\sigma $ of n increasing to infinity with n more slowly than n, we can adjust the algorithm so that, in probability, the time taken by the algorithm will be of order less than that of $n\sigma (n)$ as $n \to \infty $. The algorithm puts the n points in a cyclic order, and we also show that, with probability one, the length of the corresponding tour (that is, the sum of the n distances between adjacent points in the order given) will be asymptotic to the minimal tour length as $n \to \infty $. The latter is known (also with probability one) to be asymptotic to $\beta _k v(\mathbb{E})^p n^q $, where $\beta _k $ is a constant depending only on the dimension k, $v(\mathbb{E})$ is the volume of the set $\mathbb{E}$, $p = 1/k$, and $q = 1 - p$. Our result is stronger, and the algorithm is faster, than any other we have been able to find in the literature.
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