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# Graph planning with expected finite horizon

Chatterjee K, Doyen L. 2019. Graph planning with expected finite horizon. 34th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Symposium on Logic in Computer Science, 1–13.

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Author

Chatterjee, Krishnendu

^{ISTA}^{}; Doyen, LaurentDepartment

Abstract

Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary, to represent the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time. Consequently, our polynomial-time algorithm for adversarial stopping time also computes an optimal plan among all possible plans.

Publishing Year

Date Published

2019-06-01

Proceedings Title

34th Annual ACM/IEEE Symposium on Logic in Computer Science

Page

1-13

Conference

LICS: Symposium on Logic in Computer Science

Conference Location

Vancouver, BC, Canada

Conference Date

2019-06-24 – 2019-06-27

ISBN

IST-REx-ID

### Cite this

Chatterjee K, Doyen L. Graph planning with expected finite horizon. In:

*34th Annual ACM/IEEE Symposium on Logic in Computer Science*. IEEE; 2019:1-13. doi:10.1109/lics.2019.8785706Chatterjee, K., & Doyen, L. (2019). Graph planning with expected finite horizon. In

*34th Annual ACM/IEEE Symposium on Logic in Computer Science*(pp. 1–13). Vancouver, BC, Canada: IEEE. https://doi.org/10.1109/lics.2019.8785706Chatterjee, Krishnendu, and Laurent Doyen. “Graph Planning with Expected Finite Horizon.” In

*34th Annual ACM/IEEE Symposium on Logic in Computer Science*, 1–13. IEEE, 2019. https://doi.org/10.1109/lics.2019.8785706.K. Chatterjee and L. Doyen, “Graph planning with expected finite horizon,” in

*34th Annual ACM/IEEE Symposium on Logic in Computer Science*, Vancouver, BC, Canada, 2019, pp. 1–13.Chatterjee, Krishnendu, and Laurent Doyen. “Graph Planning with Expected Finite Horizon.”

*34th Annual ACM/IEEE Symposium on Logic in Computer Science*, IEEE, 2019, pp. 1–13, doi:10.1109/lics.2019.8785706.**All files available under the following license(s):**

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Open Access

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### Sources

arXiv 1802.03642