Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On well-partial-order theory and its application to combinatorial problems of VLSI design
SIAM Journal on Discrete Mathematics
The vertex separation number of a graph equals its path-width
Information Processing Letters
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Linear-time register allocation for a fixed number of registers
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Finding Minimal Forbidden Minors Using a Finite Congruence
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Linear Time Algorithms for k-cutwidth Problem
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Finite-State Computability of Annotations of Strings and Trees
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Cutwidth I: a linear time fixed parameter algorithm
Journal of Algorithms
Cutwidth II: algorithms for partial w-trees of bounded degree
Journal of Algorithms
An analogue of the Myhill-Nerode theorem and its use in computing finite-basis characterizations
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
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In this paper, we investigate algorithms for some related graph parameters. Each of these asks for a linear ordering of the vertices of the graph (or can be formulated as such), and constructive linear time algorithms for the fixed parameter versions of the problems have been published for several of these. Examples are cutwidth, pathwidth, and directed or weighted variants of these. However, these algorithms have complicated technical details. This paper attempts to present ideas in 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 to rederive known results for the cutwidth and the pathwidth problem, and obtain new results for several variants of these problems, like directed and weighted variants of cutwidth and modified cutwidth.