Bounding the Resource Availability of Partially Ordered Events with Constant Resource Impact

We describe a resource bounding technique called the Flow Balance Constraint (FBC) to tightly bound the amount of available resource for a set of partially ordered events with piecewise constant resource impact. We provide an efficient algorithm for calculating FBC and bound its complexity. We compare this technique with two existing resource bounding techniques, the Balance Constraint (BC) due to Laborie and the Resource Envelope (Et) due to Muscettola. We prove that using FBC to halt search under chronological search with a static variable and value order generates smaller search trees than either BC or Et. We also show that Et and BC are not strictly comparable in terms of the size of the search trees generated under chronological search with a static variable and value order. We then show how to generalize FBC to construct tighter resource bounds but at increased computational cost.