# An Algorithm to Decide Feasibility of Linear Integer Constraints Occurrng in Decision Tables

Biswas, S and Rajarman, V (1987) An Algorithm to Decide Feasibility of Linear Integer Constraints Occurrng in Decision Tables. In: IEEE Transactions on Software Engineering, 13 (12). pp. 1340-1347.

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## Abstract

Abstract-To detect errors in decision tables one needs to decide whether a given set of constraints is feasible or not. This paper describes an algorithm to do so when the constraints are linear in variables that take only integer values. Decision tables with such constraints occur frequently in business data processing and in nonnumeric applications. The aim of the algorithm is to exploit. the abundance of very simple constraints that occur in typical decision table contexts. Essentially, the algorithm is a backtrack procedure where the the solution space is pruned by using the set of simple constrains. After some simplications, the simple constraints are captured in an acyclic directed graph with weighted edges. Further, only those partial vectors are considered from extension which can be extended to assignments that will at least satisfy the simple constraints. This is how pruning of the solution space is achieved. For every partial assignment considered, the graph representation of the simple constraints provides a lower bound for each variable which is not yet assigned a value. These lower bounds play a vital role in the algorithm and they are obtained in an efficient manner by updating older lower bounds. Our present algorithm also incorporates an idea by which it can be checked whether or not an (m - 2)-ary vector can be extended to a solution vector of m components, thereby backtracking is reduced by one component.

Item Type: Journal Article Copyright 1987 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Integer programming,Backtrack algorithm,decision tables, detection of errors. Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation) 27 May 2009 12:05 13 Oct 2011 07:14 http://eprints.iisc.ernet.in/id/eprint/20330