Nonconstructive advances in polynomial-time complexity
Information Processing Letters
Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Graph minors. IV. Tree-width and well-quasi-ordering
Journal of Combinatorial Theory Series B
On well-partial-order theory and its application to combinatorial problems of VLSI design
SIAM Journal on Discrete Mathematics
Riemann's hypothesis and tests for primality
Journal of Computer and System Sciences
Exact and Approximate Solutions for the Gate Matrix Layout Problem
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Fast Fixed-Parameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Constructive Linear Time Algorithms for Small Cutwidth and Carving-Width
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
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
On Random Intersection Graphs: The Subgraph Problem
Combinatorics, Probability and Computing
Cutwidth I: a linear time fixed parameter algorithm
Journal of Algorithms
Cutwidth II: algorithms for partial w-trees of bounded degree
Journal of Algorithms
Genome-Scale Computational Approaches to Memory-Intensive Applications in Systems Biology
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover
Discrete Applied Mathematics
Innovative computational methods for transcriptomic data analysis
Proceedings of the 2006 ACM symposium on Applied computing
ACM Transactions on Algorithms (TALG)
Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover
Discrete Applied Mathematics
Cutwidth I: A linear time fixed parameter algorithm
Journal of Algorithms
Cutwidth II: Algorithms for partial w-trees of bounded degree
Journal of Algorithms
Graph coloring and the immersion order
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Fast minor testing in planar graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Effective computation of immersion obstructions for unions of graph classes
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Effective computation of immersion obstructions for unions of graph classes
Journal of Computer and System Sciences
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Recent advances in well-quasi-order theory have troubling consequences for those who would equate tractability with polynomial-time complexity. In particular, there is no guarantee that polynomial-time algorithms can be found just because a problem has been shown to be decidable in polynomial time. We present techniques for dealing with this unusual development. Our main results include a general construction strategy with which low-degree polynomial-time algorithms can now be produced for almost all of the catalogued algorithmic applications of well-quasi-order theory. We also prove that no such application of this theory can settle N @? NP nonconstructively by any established method of argument.