Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
The NP-completeness column: an ongoing guide
Journal of Algorithms
Nonconstructive advances in polynomial-time complexity
Information Processing Letters
Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Fast self-reduction algorithms for combinatorial problems of VLSI design
VLSI Algorithms and Architectures
Graph minors. IV. Tree-width and well-quasi-ordering
Journal of Combinatorial Theory Series B
Layout permutation problems and well-partially-ordered sets
Proceedings of the fifth MIT conference on Advanced research in VLSI
Finite-basis theorems and a computation-integrated approach to obstruction set isolation
Proceedings of the third conference on Computers and mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Issues in the Study of Graph Embeddings
WG '80 Proceedings of the International Workshop on Graphtheoretic Concepts in Computer Science
Fast Search Algorithms for Layout Permutation Problems
Fast Search Algorithms for Layout Permutation Problems
Obstruction set isolation for layout permutation problems
Obstruction set isolation for layout permutation problems
Extremal Graph Theory
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Capture of an intruder by mobile agents
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the maximum clique minor and some subgraph homeomorphism problems
Theoretical Computer Science
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Searching cycle-disjoint graphs
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Arc searching digraphs without jumping
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Fast searching games on graphs
Journal of Combinatorial Optimization
Fixed-Parameter tractability, a prehistory,
The Multivariate Algorithmic Revolution and Beyond
The birth and early years of parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
Linear time algorithm for computing a small biclique in graphs without long induced paths
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Lower bounds on edge searching
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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Recent advances in well-partial-order theory, especially the seminal contributions of Robertson and Seymour, have troubling consequences for those who would equate tractability with polynomial-time decidability. Specifically:many problems are now known to be decidable in low-degree polynomial time, but only by decision algorithms with overwhelmingly astronomical constants of proportionality,the existence of such a polynomial-time decision algorithm alone does not ensure that a corresponding search problem can be solved efficiently, andeven if both a decision problem and a corresponding search problem can be shown to be polynomial-time computable, there is no guarantee that correct algorithms can be found or even recognized within any bounded amount of time.In this paper, we present a number of techniques for dealing with these remarkable features of algorithms based on well-partially-ordered sets. Our main results include a general strategy with which such algorithms can be made constructive. With the aid of this method, we demonstrate that low-degree polynomial-time algorithms are now known for almost all of the catalogued applications of RS posets. We also prove that, despite the nonconstructive nature of the well-partial-order theory on which this line of research is based, no RS poset application can settle P @@@@ N P non-constructively by any established method of argument.