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Partial (Neighbourhood) Singleton Arc Consistency for Constraint Satisfaction Problems

Wallace Richard J.

Fundamenta Informaticae

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2020

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Vol. 174, nr 3/4

311--344

EN

Algorithms based on singleton arc consistency (SAC) show considerable promise for improving backtrack search algorithms for constraint satisfaction problems (CSPs). The drawback is that even the most efficient of them is still comparatively expensive. Even when limited to preprocessing, they give overall improvement only when problems are quite difficult to solve with more typical procedures such as maintained arc consistency (MAC). The present work examines a form of partial SAC and neighbourhood SAC (NSAC) in which a subset of the variables in a CSP are chosen to be made SAC-consistent or neighbourhood-SAC-consistent. Such consistencies, despite their partial character, are still well-characterized in that algorithms have unique fixpoints. Heuristic strategies for choosing an effective subset of variables are described and tested, the best being choice by highest degree and a more complex strategy of choosing by constraint weight after random probing. Experimental results justify the claim that these methods can be nearly as effective as the corresponding full version of the algorithm in terms of values discarded or problems proven unsatisfiable, while significantly reducing the effort required to achieve this.

2

On certain properties of neighborhoods of analytic functions of complex order

Latha S., Poornima N.

Journal of Mathematics and Applications

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2008

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Vol. 30

83-90

EN

Let A(n) denote the class of functions of the form [wzór] which are analytic in the open unit disk U = {z : |z| < 1}. In this note, the subclasses Sn (β, γ, a, c), Rn (β, γ, a, c; μ ), S(sup α) (sub n) (β, γ a, c) and R (sup α) (sub n) (β, γ, a, c; μ ) of A(n)(are defined and some properties of neighborhoods arę studied for functions of complex order in these classes.

3

On certain subclasses of meromorphically p-valent functions

Lashin A.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

371-380

EN

In this paper we introduce the class [...](A B) of meromorphically p-valent functions and investigate some inclsion properties, coefficient estimates, distortion theorems. Also we investigate some results concerning the partial sums and nieghbourhoods of such functions.

4

On certain subclasses of meromorphically multivalent functions associated with a certain linear operator

Aouf M. K., Murugusundaramoorthy G.

Journal of Mathematics and Applications

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2007

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Vol. 29

33-52

EN

In this paper we introduce and study two subclasses (Rn,p(α, A, B)) and Sn,p(α, A, B)) of meromorphic p-valent functions of order α (0 ≤ α < p) defined by certain linear operator. We investigate the various important properties and characteristics of these subclasses. Some properties of neighborhoods of functions in these subclasses are investigated. Also we derive many interesting results for the Hadamard products of functions belonging to the class Sn,p(α, A, B).