Abstract
The idea of applying a dynamic programming strategy to evaluating certain objective functions on trees is fairly straightforward. The road for this idea to develop into theories of width parameters has been not so straight. Hans Bodlaender has played a major role in the process of mapping out that road. In this sentimental journey, we will recount our collective road trip over the past decades.
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References
Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in k-trees. SIAM J. Algebraic Discrete Methods 8(2), 277–284 (1987)
Arnborg, S., Hedetniemi, S.T., Proskurowski, A.: Algorithms on graphs with bounded treewidth. Discrete Appl. Math. 54(2–3) (1994)
Arnborg, S., Lagergren, J., Seese, D.: Easy problems for tree-decomposable graphs. J. Algorithms 12, 308–340 (1991)
Arnborg, S., Proskurowski, A.: Problems on graphs with bounded decomposability. In: Proceedings of the 17th South-Eastern Conference on Combinatorics, Graph Theory and Computing, Utilitas Mathematica, Winnipeg, Congressus Numerantium, vol. 53, pp. 167–170 (1986)
Arnborg, S., Proskurowski, A.: Characterization and recognition of partial 3-trees. SIAM J. Algebraic. Discrete Methods 7(2), 305–314 (1986)
Arnborg, S., Proskurowski, A., Corneil, D.G.: Forbidden minors characterization of partial 3-trees. In: Proceedings of the Seventh Hungarian Colloquium on Combinatorics, Colloquia Mathematica Societatis Janos Bolyai, vol. 52, pp. 49–62 (1988)
Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. In: Proceedings of 25th Symposium on the Theory of Computing (STOC 1993), pp. 226–234 (1993)
Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybern. 11, 1–21 (1993)
Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci. 209, 1–45 (1998)
Bodlaender, H.L.: Treewidth of graphs: 1987; Arnborg, Corneil, Proskurowski. In: Kao, M.-Y. (ed.) Encyclopedia of Algorithms, pp. 968–970. Springer, New York (2008). https://doi.org/10.1007/978-0-387-30162-4
Bodlaender, H.L., Fomin, F.V.: Tree decompositions with small cost. Discrete Appl. Math. 145(2), 143–154 (2005)
Colbourn, C.J., Proskurowski, A.: Concurrent transmissions in broadcast networks. In: Paredaens, J. (ed.) ICALP 1984. LNCS, vol. 172, pp. 128–136. Springer, Heidelberg (1984). https://doi.org/10.1007/3-540-13345-3_11
Kennelly, A.E.: Equivalence of triangles and three-pointed stars in conducting networks. Electr. World Eng. 34, 413–414 (1899)
MacMahon: The combination of resistances, The Electrician, 8 April (1892)
van Rooij, J.M.M., Bodlaender, H.L., Rossmanith, P.: Dynamic programming on tree decompositions using generalised fast subset convolution. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 566–577. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04128-0_51
Wald, J.A., Colbourn, C.J.: Computing reliability for a generalization of series-parallel networks. In: Proceedings of the Twentieth Allerton Conference on Communication, Control, and Computing, pp. 25–26 (1982)
Yannakakis, M.: Computing the minimum fill-in is NP-complete. SIAM J. Algebraic Discrete Methods 2(1), 77–79 (1981)
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Arnborg, S., Proskurowski, A. (2020). Seeing Arboretum for the (partial k-) Trees. In: Fomin, F.V., Kratsch, S., van Leeuwen, E.J. (eds) Treewidth, Kernels, and Algorithms. Lecture Notes in Computer Science(), vol 12160. Springer, Cham. https://doi.org/10.1007/978-3-030-42071-0_1
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