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This paper deals with distributed graph algorithms. Processors reside in the vertices of a graph G and communicate only with their neighbors. The system is synchronous and reliable, there is no limit on message lengths and local computation is instantaneous. The results: A maximal independent set in an n-cycle cannot be found faster than Ω(log* n) and this is optimal by [CV]. The d-regular tree of...
We describe a parallel algorithm for testing a graph for planarity, and for finding an embedding of a planar graph. For a graph on n vertices, the algorithm runs in O(log2 n) steps on n processors of a parallel RAM. The previous best algorithm for planarity testing in parallel polylog time ([Ja'Ja' and Simon, 82]) used a reduction to solving linear systems, and hence required Ω(n2..49...) processors...
A polynomial time isomorphism test for a class of groups, properly containing the class of abelian groups, is presented. Isomorphism testing of group presentations for (a subclass of) the same class of groups is shown to be (graph) isomorphism complete. These seem to be the first known isomorphism complete problems in group theory. Subexponential tests are presented as well for rings and algebras.
We consider problems in computational geometry when every one of the input points is moving in a prescribed manner. We present and analyze efficient algorithms for a number of problems and prove lower bounds for some of them.
An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.
This standard applies to all oil-immersed or dry-type, single-phase or three-phase outdoor or indoor shunt reactors rated 501 kVA and larger. It covers general requirements, terminology, ratings, insulation classes, dielectric tests, losses, impedance, temperature rise, construction, accessories and the test code.<<ETX>>
Suppose we are given a set of generators for a group G of permutations of a colored set A. The color automorphism problem for G involves finding generators for the subgroup of G which stabilizes the color classes. Testing isomorphism of graphs of valence ≤ t is polynomial-time reducible to the color automorphism problem for groups with small simple sections. The algorithm for the latter problem involves...
We show how to prove (and disprove) theorems in the initial algebra of an equational variety by a simple extension of the Knuth-Bendix completion algorithm. This allows us to prove by purely equational reasoning theorems whose proof usually requires induction. We show applications of this method to proofs of programs computing over data structures, and to proofs of algebraic summation identities....
Canonical labelling of graphs (CL, for short) can be used, e.g., to test isomorphism. We prove that a simple vertex classification procedure results after only two refinement steps in a CL of random graphs with probability 1 - exp(-cn). With a slight modification we obtain a linear time CL algorithm with only exp(-cn log n/log log n) probability of failure. An additional depth-first search yields...
This standard was prepared by the Gyro and Accelerometer Panel of the Aerospace Electronics Systems Group of the Institute of Electrical and Electronics Engineers. It consists of two parts. Part I is a specification format guide for the preparation of an accelerometer specification. It provides a common meeting ground of terminology and practice for manufacturers and users. Part II is a compilation...
A new model of abstract automata is presented employing the concept of finite automata on a network. Each normal network n provided with a one-way input tape determines a family of languages nl. A representation theorem, analogous to the Chomsky-Schützenberger representation theorem for context free languages1, is proved for the class nl. One consequence is that nl is a principal full AFL generated...
In the first part of this paper, an algorithm is derived for testing a given two state machine for the property of being universal. Various characterizations of universality are also obtained, and are stated in the form of necessary and sufficient conditions. The second part of this paper is concerned with the economical realization of sequential machines as networks of identical modules. Bounds are...
Not all switching functions are realizable by a single cascade of 2- input, 1-output switching elements, even if repeated inputs are allowed. However, arrays of such cascades feeding a single collector cascade of AND or OR cells can be used to synthesize any function. This paper is concerned with optimal array realizations of this form. A procedure is given which allows one to generate rather efficiently...
A regular event W is a star event iff there exists another event V such that W = V*. In that case, V is called a root of W. It is shown that every regular event has a unique minimum root, which is contained in every other root of W. An algorithm for finding the minimum root is presented, and the root is shown to be regular. The results have applications to languages, codes, canonical forms for regular...
This paper introduces several new concepts which are applicable to the problem of diagnosis of equipment failures. Following the definitions of an equipment, an element of the equipment, and the model of a test, a general diagram of a testing procedure is developed. The testing diagram is constructed in such a way that the various tests needed and the probability of failure of the elements are readily...
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