A Comparative Study of Arithmetic Constraints on Integer Intervals

Abstract

We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that reduce the variable domains. We compare these approaches using a set of benchmarks.

An Analysis of Arithmetic Constraints on Integer Intervals

“…The maximum value the expression on the right-hand side can take is 3 √ 140 , so we conclude x ≤ 5. By reusing (3), now with the information that x ∈ [1..5], we conclude that the maximum value the expression on the right-hand side of (3) can take is actually 3 √ 45 , from which it follows that x ≤ 3.…”

Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model

“…Apt and Zoeteweij [3] have defined the following arithmetic operations on 110 integer intervals A and B:…”