... graph¹

A relaxed planning graph is a planning graph with no action pairs marked as mutex.

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... graph.²

A serial planning graph is a planning graph with every pair of non-noop actions at the same level marked as mutex.

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... ``LR''³

The original notation for this ordering criterion is LC for ``least (repair) cost'', where the repair cost is defined to be the number of refinements. Because we introduce a new ordering criterion based on heuristic cost, we choose to rename this ordering criterion.

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....⁴

In contrast, Vere's DEVISER can only handle duration constraints of the form $\delta_{i}^{}$ = c.

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... actions⁵

There were two types of domains with durative actions at IPC3: ``SimpleTime'' domains having actions with constant duration and ``Time'' domains with durations being functions of action parameters. The results with durative actions presented in this paper are for ``SimpleTime'' domains as there is currently no support for durations as functions of action parameters in VHPOP. It would, in principle, not be hard to add such support though, and we expect future versions of VHPOP to have it.

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...tab:stquality).⁶

The poor performance is in part also due to the use of 1 for $\epsilon$ (see Section 4) in VHPOP, while most other planners used 0.01 or less. Using 0.01 for $\epsilon$ with VHPOP reduces the total execution time of plans with about 15 percent.

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... effort.⁷

The latest version of VHPOP is available for download at www.cs.cmu.edu/~lorens/vhpop.html.

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