The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs

• Published in: Theoretical computer science Vol. 244; no. 1; pp. 167 - 188
• Main Authors: Bodlaender, Hans L., Fellows, Michael R., Hallett, Michael T., Wareham, H.Todd, Warnow, Tandy J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 06-08-2000; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Analytical, structural and metabolic biochemistry; Applied sciences; Biological and medical sciences; Classical combinatorial problems; Combinatorics; Combinatorics. Ordered structures; Complexity; Computer science; control theory; systems; Dna, deoxyribonucleoproteins; Exact sciences and technology; Fixed parameter intractability; Fundamental and applied biological sciences. Psychology; Graph problems; Graph theory; Mathematics; Nucleic acids; Sciences and techniques of general use; Theoretical computing; Triangulation of colored graphs; Fixed parameter intractability; Triangulation of colored graphs; Graph problems; Complexity; Graph decomposition; Tree(graph); Combinatorial problem; Graph colouring; Graph theory; Phylogeny; Pathwidth; Computational complexity
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/S0304-3975(98)00342-9

In this paper, we consider the complexity of a number of combinatorial problems; namely,
Intervalizing
Colored
Graphs (DNA
physical mapping),
Triangulating
Colored
Graphs
(perfect phylogeny), (
Directed) (
Modified)
Colored
Cutwidth,
Feasible
Register
Assignment and
Module
Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in “yes”-instances. For all of these problems with the exceptions of
Feasible
Register
Assignment and
Module
Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes
W[t] for all
t∈
N
. We also show that
Intervalizing
Colored
Graphs,
Triangulating
Colored
Graphs, and
Colored
Cutwidth are NP-Complete.