A polynomial algorithm for the min-cut linear arrangement of trees
Journal of the ACM (JACM)
Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On minimizing width in linear layouts
Discrete Applied Mathematics
Graphs with small bandwidth and cutwidth
Discrete Mathematics
On well-partial-order theory and its application to combinatorial problems of VLSI design
SIAM Journal on Discrete Mathematics
Tree-width, path-width, and cutwidth
Discrete Applied Mathematics
Designing multi-commodity flow trees
Information Processing Letters
Improved self-reduction algorithms for graphs with bounded treewidth
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Regular Article: On search, decision, and the efficiency of polynomial-time algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Divide-and-conquer approximation algorithms via spreading metrics
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A Polynomial Time Algorithm for the Cutwidth of Bounded Degree Graphs with Small Treewidth
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Characterizing graphs of small carving-width
Discrete Applied Mathematics
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Consider the following problem: For any constant k and any input graph G, check whether there exists a tree T with internal vertices of degree 3 and a bijection χ mapping the vertices of G to the leaves of T such that for any edge of T, the number of edges of G whose end-points have preimages in different components of T - e, is bounded by k. This problem is known as the MINIMUM ROUTING TREE CONGESTION problem and is relevant to the design of minimum congestion telephone networks. If, in the above definition, we consider lines instead of trees with internal vertices of degree 3 and bijections mapping the vertices of G to all the vertices of T, we have the well known MINIMUM CUT LINEAR ARRANGEMENT problem. Recent results of the Graph Minor series of Robertson and Seymour imply (non-constructively) that both these problems are fixed parameter tractable. In this paper we give a constructive proof of this fact. Moreover, the algorithms of our proof are optimal and able to output the corresponding pair (T, χ) in case of an affirmative answer.