# Classical Dynamic Controllability Revisited - A Tighter Bound on the Classical Algorithm

### Mikael Nilsson, Jonas Kvarnström, Patrick Doherty

#### Abstract

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are uncontrollable (determined by nature), as is often the case for actions in planning. It is essential to verify that such networks are dynamically controllable (DC) – executable regardless of the outcomes of uncontrollable durations – and to convert them to an executable form. We use insights from incremental DC verification algorithms to re-analyze the original verification algorithm. This algorithm, thought to be pseudo-polynomial and subsumed by an O(n5) algorithm and later an O(n4) algorithm, is in fact O(n4) given a small modification. This makes the algorithm attractive once again, given its basis in a less complex and more intuitive theory. Finally, we discuss a change reducing the amount of work performed by the algorithm.

#### References

- Cormen, T. H., Stein, C., Rivest, R. L., and Leiserson, C. E. (2001). Introduction to Algorithms. McGraw-Hill.
- Dechter, R., Meiri, I., and Pearl, J. (1991). Temporal constraint networks. Art. Int., 49(1-3):61-95.
- Hunsberger, L. (2010). A fast incremental algorithm for managing the execution of dynamically controllable temporal networks. In Proc. TIME.
- Hunsberger, L. (2013). A faster execution algorithm for dynamically controllable STNUs. In Proc. TIME.
- Morris, P. (2006). A structural characterization of temporal dynamic controllability. In Proc. CP.
- Morris, P. and Muscettola, N. (2005). Temporal dynamic controllability revisited. In Proc. AAAI.
- Morris, P., Muscettola, N., and Vidal, T. (2001). Dynamic control of plans with temporal uncertainty. In Proc. IJCAI.
- Muscettola, N., Morris, P., and Tsamardinos, I. (1998). Reformulating temporal plans for efficient execution. In Proc. KR.
- Nilsson, M., Kvarnström, J., and Doherty, P. (2013). Incremental dynamic controllability revisited. In Proc. ICAPS.
- Shah, J. A., Stedl, J., Williams, B. C., and Robertson, P. (2007). A fast incremental algorithm for maintaining dispatchability of partially controllable plans. In Proc. ICAPS.
- Stedl, J. (2004). Managing temporal uncertainty under limited communication: A formal model of tight and loose team coordination. Master's thesis, MIT.
- Stedl, J. and Williams, B. (2005). A fast incremental dynamic controllability algorithm. In Proc. ICAPS Workshop on Plan Execution: A Reality Check.
- Vidal, T. and Ghallab, M. (1996). Dealing with uncertain durations in temporal constraints networks dedicated to planning. In Proc. ECAI.

#### Paper Citation

#### in Harvard Style

Nilsson M., Kvarnström J. and Doherty P. (2014). **Classical Dynamic Controllability Revisited - A Tighter Bound on the Classical Algorithm** . In *Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-758-015-4, pages 130-141. DOI: 10.5220/0004815801300141

#### in Bibtex Style

@conference{icaart14,

author={Mikael Nilsson and Jonas Kvarnström and Patrick Doherty},

title={Classical Dynamic Controllability Revisited - A Tighter Bound on the Classical Algorithm},

booktitle={Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2014},

pages={130-141},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004815801300141},

isbn={978-989-758-015-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - Classical Dynamic Controllability Revisited - A Tighter Bound on the Classical Algorithm

SN - 978-989-758-015-4

AU - Nilsson M.

AU - Kvarnström J.

AU - Doherty P.

PY - 2014

SP - 130

EP - 141

DO - 10.5220/0004815801300141