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It is shown that the external path length of a binary tree is closely related to the ratios of means of certain integers and establish the upper bound External Path Length≤N log 2 N+ D - log 2 D -0.6623 , where N denotes the number of external nodes in the tree and D is the difference in length...
Inductive inference machines construct programs for total recursive functions given only example values of the functions. Probabilistic inductive inference machines are defined, and for various criteria of successful inference, it is asked whether a probabilistic inductive inference machine can...
An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ↿ F ↾ into n pieces F i , l ≤ i ≤ n , each of length ↿ F i ↾ = L / m , so that every m pieces suffice for reconstructing F . Dispersal and reconstruction are computationally efficient. The sum of...
Today's standard model for database concurrency control, called serializability theory, represents executions of transactions as partial orders of operations. The theory tells when an execution is serializable, that is, when the set of operations of a transaction execute atomically with respect...
The prefix problem consists of computing all the products x 0 x 1 … x j ( j = 0, … , N - 1), given a sequence x = ( x 0 , x 1 , … , x N- 1 ) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with Boolean networks, which are...
In 1979, G. K. Manacher showed that the Ford-Johnson sorting algorithm FJA, acting on t real numbers, can be beaten for an infinite set of values t . These values form a partial cover of constant density not close to 1 over an initial sequence of each band running from u k = ⌊(4/3)2 k ⌋ to u...
It is shown that n + k - O (1) comparisons are necessary, on average, to find the k th smallest of n numbers ( k ⪇ n /2). This lower bound matches the behavior of the technique of Floyd and Rivest to within a lower-order term. 7 n /4 ± o ( n ) comparisons, on average, are shown to be necessary...
This paper gives a fast, linear-time algorithm for generating high-quality pixel representations of curved lines. The results are similar to what is achieved by selecting a circle whose diameter is the desired line width, and turning on all pixels covered by the circle as it moves along the...
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