
| problem    | #actions   | #agenda entries   | CPU( < e )   | CPU( < h )   |
|------------|------------|-------------------|--------------|--------------|
| bwlarge a  | 162        | 0.69              | 0.07         |              |
| bwww       | 242        | 5                 | 1.45         | 0.11         |
| bwlarge c  | 450        | 7                 | 4.85         | 0.22         |
| bwlarged   | 722        | 11                | 14.18        | 0.35         |
| bwlarge e  | 722        | 11                | 12.95        | 0.35         |
| bwlarge f  | 1 250      | 6                 | 44.93        | 0.58         |
| bw large g | 1 800      | g                 | 97.11        | 0.88         |
| parcplan   | 1 960      | 4                 | 25.84        | 1.47         |
| stack_20   | 800        | 19                | 6.91         | 0.36         |
| stack_40   | 3 200      | 39                | 1 60.00      | 1.74         |
| stack_60   | 7 200      | 59                | 840.42       | 4.85         |
| stack_80   | 1 2800     | 79                | 11.38        |              |

Figure 5:  Comparison of ≤ e and ≤ h on blocks world problems.  \#actions shows the number of actions in the set O , from which the planner tries to construct a plan. \#agenda entries says how many goal subsets have been detected and ordered by GAM. Column 4 and 5 display the CPU time that is required by both methods to compute the agenda when provided with the set O. A dash will always mean that IPP ran out of memory on a 1 Gbyte machine.
Figure 6 and Figure 7 show the results for the other domains, in which our method is able to detect reasonable orderings. Figure 6 lists the domains, in which both methods return the same goal agendas.  The tyreworld, hanoi, and fridgeworld domains originate from UCPOP (Penberthy & Weld, 1992), while the link-repeat domain can be found in (Veloso
& Blythe, 1994). The performance results coincide with those shown in Figure 5. Figure 7 shows the same picture in terms of runtime performance, but in these domains different agendas are returned by ≤ e and ≤ h .

The woodshop and scheduling domains contain actions with conditional effects, while the other domains only use STRIPS operators. The computation of < e fails to derive goal orderings for all scheduling world problems (of whi we only display the largest problem sched6 ) and for the wood1 problem. The explanation for this behavior can be found in the different treatment of conditional effects by both methods. IPP does only find a very limited form of mutex relations between conditional effects when building the planning graph. A goal, which is achieved with a conditional effect, will not very often be exclusive to a large nmber of other facts in the graph. Thus, the F sets are very small or sometimes even empty and consequently, only very few actions can be excluded when performing the reachability analysis and thus, reasonable orderings may remain undetected. Direct analysis investigates the conditional effects in more detail and is therefore able to derive much larger F sets.

The behavior of the <h method in the STRIPS domains bulldozer, glassworld, and shopping world is caused by the same phenomenon. In these domains, one can derive much larger F sets using planning graphs and in turn these sets exclude more actions.  Since direct analysis finds smaller or empty F sets, it also finds less ≤ h relations. The woodshop domain