# Effective scheduling of tasks under weak temporal interval constraints

## Abstract

Numerous AI planning applications and real-time system scheduling problems do not fit the traditional scenarios of the scheduling literature; instead, they are better expressed in terms of the temporal interval relations between the tasks. Given a set of tasks and a set of constraints expressed in terms of the atomic temporal interval relations, the problem of finding the shortest consistent schedule often arises. In the most general situation, the interval constraints leave some degree of uncertainty: the problem is under-specified. It is first shown herein that, in the completely specified case, the greatest lower bound of all schedule lengths can be calculated as the “*Size*” of a chain of intervals playing a role similar to that of a critical path in the familiar critical path analysis. Subsequently, a heuristic search algorithm is presented to reduce the general under-determined case to a completely specified one.

## Key words

Constraint Propagation Planning Real-Time Systems Scheduling Temporal Interval Relations Temporal Reasoning## Preview

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