Abstract
This paper investigates algorithms for some related graph parameters. Each asks for a linear ordering of the vertices of the graph (or can be formulated as such), and there are constructive linear time algorithms for the fixed parameter versions of the problems. Examples are cutwidth, pathwidth, and directed or weighted variants of these. However, these algorithms have complicated technical details. This paper attempts to present these algorithms in a different more easily accessible manner, by showing that the algorithms can be obtained by a stepwise modification of a trivial hypothetical non-deterministic algorithm.
The methodology is applied for a generalisation of the cutwidth problem to weighted mixed graphs. As a consequence, we obtain new algorithmic results for various problems like modified cutwidth, and rederive known results for other related problems with simpler proofs.
The first and third author were partially supported by EC contract IST-1999-14186: Project ALCOM-FT (Algorithms and Complexity – Future Technologies. The second author was supported by the New Zealand Marsden Fund, and the Australian Research Council Project DP0344762. The research of the third author was supported by the Spanish CICYT project TIC2000-1970-CE and the Ministry of Education and Culture of Spain (Resolución 31/7/00 – BOE 16/8/00).
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Bodlaender, H.L., Fellows, M.R., Thilikos, D.M. (2003). Starting with Nondeterminism: The Systematic Derivation of Linear-Time Graph Layout Algorithms. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_18
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DOI: https://doi.org/10.1007/978-3-540-45138-9_18
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