Propagating Resource Constraints Using Mutual Exclusion Reasoning Romeo Sanchez 1 , Minh B. Do 1 , and Jeremy Frank 2 1 Arizona State University , Tempe AZ 85287-5406, USA, rsanchez,binhminh@asu.edu 2 NASA Ames Research Center, Mail Stop N269-3, Moffet Field, CA 94035-1000, USA, frank@ptolemy.arc.nasa.gov Abstract. One of the most recent techniques for propagating resource constraints in Constraint Based scheduling is Energy Constraint. This technique focuses in precedence based scheduling, where precedence relations are taken into account rather than the absolute position of activities. Although, this particular technique proved to be efficient on discrete unary resources, it provides only loose bounds for jobs using discrete multi-capacity resources. In this paper we show how mu- tual exclusion reasoning can be used to propagate time bounds for activities using discrete resources. We show that our technique based on critical path analysis and mutex reasoning is just as effective on unary resources, and also shows that it is more effective on multi-capacity resources, through both examples and empirical study. 1 Introduction Scheduling problems are fundamentally concerned with the interaction of temporal con- straints and resource constraints. Tasks that require the same resources lead to a choice of precedence, but some choices may be impossible due to the absolute and relative constraints on the timing of activities. A number of techniques have been developed to propagate resource and temporal constraints. Laborie [1] provides a good survey of these results, including Timetabling [2], Edge Finding [3, 4], and Energetic Reasoning [8]. Based on the survey, Laborie developed a technique called the Energy Precedence Constraint (EC). This constraint works on resources that are used then released (called discrete resources by Laborie). The idea is to estimate the time required to execute all activities on a single resource by computing the “energy”, that is the sum of the dura- tion of the activities times the amount of the resource they require, then computing the minimum duration by dividing the energy by the amount of the resource available. The EC is simple to compute, but results in loose computational bounds in cases where the total capacity of a resource is exceeded by the resource consumption of the activities. We observe that a simple analysis of the activities can lead to the discovery of mutual exclusions among group of activities. This can result in improved bounds on such problems with small cost. The rest of the paper is organized as follows. Section 2 introduces the preliminaries of our work, and a short description of the energy bound EB propagated by the energy constraint procedure. Section 3 will describe the idea of our constraint propagation tech- nique called CPMB (critical path plus mutex bounds), and one extension for multiple machine multiple capacity problems, called GMB (group mutex bounds). Then, Sec- tion 4 presents an example and the possible best and worst case scenarios for the prop- agation techniques described in this paper. Section 5 will introduce some aspects of our implementation which affect the way resource constraints get propagated. Section 6 will