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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References
Bast, H., Hert, S.: The area partitioning problem. In: Proc. 12th Can. Conf. Comput. Geom. (CCCG 2000), Fredericton, NB, Canada, pp. 163–171 (2000)
Baumann, N., Skutella, M.: Earliest arrival flows with multiple sources. Math. Oper. Res. 34(2), 499–512 (2009); Journal version of 2006 FOCS article Solving evacuation problems efficiently
Becker, R., Lari, I., Lucertini, M., Simeone, B.: Max-min partitioning of grid graphs into connected components. Networks 32(2), 115–125 (1998)
Fekete, S.P., Gray, C., Kröller, A.: Evacuation of rectilinear polygons. Technical report (2010), http://arxiv.org/abs/1008.4420
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics 17, 416–429 (1969)
Györi, E.: On division of graphs to connected subgraphs. Combinatorics, Keszthely, 485–494 (1978)
Lovász, L.: A homology theory for spanning trees of a graph. Acta Mathematica Hungarica 30(3), 241–251 (1977)
Lumelsky, V.: Polygon area decomposition for multiple-robot workspace division. Int. Journal of Computational Geometry and Applications 8(4), 437–466 (1998)
Ma, J., Ma, S.: An O(k 2 n 2) algorithm to find a k-partition in a k-connected graph. Journal of Computer Science and Technology 9(1), 86–91 (1994)
Moore, C., Robson, J.: Hard tiling problems with simple tiles. Discrete and Computational Geometry 26(4), 573–590 (2001)
Salgado, L.R., Wakabayashi, Y.: Approximation results on balanced connected partitions of graphs. Electr. Notes in Discrete Mathematics 18, 207–212 (2004)
Skutella, M.: An introduction to network flows over time. In: Research Trends in Combinatorial Optimization, pp. 451–482. Springer, Heidelberg (2009)
Suzuki, H., Takahashi, N., Nishizeki, T.: A linear algorithm for bipartition of biconnected graphs. Information Processing Letters 33(5), 227–231 (1990)
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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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