Abstract
Path-decompositions of graphs are an important ingredient of dynamic programming algorithms for solving efficiently many NP-hard problems. Therefore, computing the pathwidth and associated path-decomposition of graphs has both a theoretical and practical interest. In this paper, we design a Branch and Bound algorithm that computes the exact pathwidth of graphs and a corresponding path-decomposition. Our main contribution consists of several non-trivial techniques to reduce the size of the input graph (pre-processing) and to cut the exploration space during the search phase of the algorithm. We evaluate experimentally our algorithm by comparing it to existing algorithms of the literature. It appears from the simulations that our algorithm offers a significative gain with respect to previous work. In particular, it is able to compute the exact pathwidth of any graph with less than 60 nodes in a reasonable running-time (≤ 10 min.). Moreover, our algorithm achieves good performance when used as a heuristic (i.e., when returning best result found within bounded time-limit). Our algorithm is not restricted to undirected graphs since it actually computes the vertex-separation of digraphs (which coincides with the pathwidth in case of undirected graphs).
This work has been partially supported by European Project FP7 EULER, ANR project Stint (ANR-13-BS02-0007), the associated Inria team AlDyNet and the project ECOS-Sud Chile.
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References
Biedl, T.C., Bläsius, T., Niedermann, B., Nöllenburg, M., Prutkin, R., Rutter, I.: Using ILP/SAT to determine pathwidth, visibility representations, and other grid-based graph drawings. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 460–471. Springer, Heidelberg (2013)
Bodlaender, H.L., Fomin, F.V., Koster, A.M., Kratsch, D., Thilikos, D.M.: A note on exact algorithms for vertex ordering problems on graphs. Theory Comput. Syst. 50(3), 420–432 (2012)
Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Kernel bounds for structural parameterizations of pathwidth. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 352–363. Springer, Heidelberg (2012)
Bodlaender, H.L., Kloks, T.: Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms 21(2), 358–402 (1996)
Bodlaender, H.L., Koster, A.M.C.A.: Treewidth computations ii. lower bounds. Inf. Comput. 209(7), 1103–1119 (2011)
Coudert, D., Huc, F., Mazauric, D., Nisse, N., Sereni, J.-S.: Reconfiguration of the routing in WDM networks with two classes of services. In: Optical Network Design and Modeling (ONDM), pp. 1–6. IEEE (2009)
Coudert, D., Mazauric, D., Nisse, N.: Experimental evaluation of a branch and bound algorithm for computing pathwidth. Tech. Rep. RR-8470. Inria (February 2014)
Díaz, J., Petit, J., Serna, M.: A survey on graph layout problems. ACM Comput. Surveys 34(3), 313–356 (2002)
Duarte, A., Escudero, L.F., Martí, R., Mladenovic, N., Pantrigo, J.J., Sánchez-Oro, J.: Variable neighborhood search for the vertex separation problem. Computers & OR 39(12), 3247–3255 (2012)
Hein, A., Koster, A.M.C.A.: An experimental evaluation of treewidth at most four reductions. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 218–229. Springer, Heidelberg (2011)
MIPLIB - mixed integer problem library, http://miplib.zib.de/ .
Rome graphs, http://www.graphdrawing.org/download/rome-graphml.tgz
Skodinis, K.: Construction of linear tree-layouts which are optimal with respect to vertex separation in linear time. J. Algorithms 47(1), 40–59 (2003)
Solano, F., Pióro, M.: Lightpath reconfiguration in WDM networks. IEEE/OSA J. Opt. Commun. Netw. 2(12), 1010–1021 (2010)
Stein, W., et al.: Sage Mathematics Software (Version 6.0). The Sage Development Team (2013), http://www.sagemath.org
VSPLIB (2012), http://www.optsicom.es/vsp/
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Coudert, D., Mazauric, D., Nisse, N. (2014). Experimental Evaluation of a Branch and Bound Algorithm for Computing Pathwidth. In: Gudmundsson, J., Katajainen, J. (eds) Experimental Algorithms. SEA 2014. Lecture Notes in Computer Science, vol 8504. Springer, Cham. https://doi.org/10.1007/978-3-319-07959-2_5
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DOI: https://doi.org/10.1007/978-3-319-07959-2_5
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