Abstract
We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the “confluent” context in which the routes to exits remain fixed over time, and the “non-confluent” context in which routes may change. Confluent evacuation plans are simpler to carry out, as they allocate contiguous regions to exits; non-confluent allocation can possibly create faster evacuation plans. We give results on the hardness of creating the evacuation plans and strongly polynomial algorithms for finding confluent evacuation plans when the building has two exits. We also give a pseudo-polynomial time algorithm for non-confluent evacuation plans. Finally, we show that the worst-case bound between confluent and non-confluent plans is \(2-O(\frac{1}{k})\).
This research was funded by the German Ministry for Education and Research (BMBF) under grant number 03NAPI4 “ADVEST”, which fully funded Chris Gray.
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Fekete, S., Gray, C., Kröller, A. (2010). Evacuation of Rectilinear Polygons. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_3
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DOI: https://doi.org/10.1007/978-3-642-17458-2_3
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