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

AbstractIn 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

The Parameterized Complexity of Some Problems in Logic and Linguistics (Extended Abstract)

March 1, 2002 Rodney G. Downey Department of Mathematics, Victoria University P.O. Box 600, Wellington, New Zealand [email protected] Michael R. Fellows, Bruce M. Kapron and Michael T. Hallett Department of Computer Science, University of Victoria Victoria, British Columbia V8W 3P6 Canada contact author: [email protected] H. Todd Wareham Department of Computer Science Memorial University of Newfoundland St. Johns, Newfoundland A1C 5S7 Canada [email protected] Summary The theory of parameterized computational complexity introduced in [DF1-3] appears to be of wide applicability in the study of the complexity of concrete problems [ADF,BFH,DEF,FHW,FK]. We believe the theory may be of particular importance to practical applications of logic formalisms in programming language design and in system specification. The reason for this relevance is that while many computational problems in logic are extremely intractable generally, realistic applications often involve a "hidden parameter" according to which the computational problem may be feasible according to the more sensitive criteria of fixed-parameter tractability that is the central issue in parameterized computational complexity. We illustrate how this theory may apply to problems in logic, programming languages and linguistics by describing some examples of both tractability and intractability results in these areas. It is our strong expectation that these results are just the tip of the iceberg of interesting applications of parameterized complexity theory to logic and linguistics. The main results described in this abstract are as follows. (1) The problem of determining whether a word x can be derived in k steps in a context-sensitive grammar G (Short CSL Derivation) is complete for the paramet..