Michael R. Fellows

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Parameterized complexity is a new and promising approach to the central issue of how to cope with problems that are NP-hard or worse — as is so frequently the case in the natural world of computing. The key idea is to isolate some aspect(s) or part(s) of the input as the parameter, and to confine the seemingly inevitable combinatorial explosion of(More)
Kernelization is a central technique used in parameterized algorithms, and in other techniques for coping with NP-hard problems. In this paper, we introduce a new method which allows us to show that many problems do not have polynomial size kernels under reasonable complexity-theoretic assumptions. These problems include kPath, k-Cycle, k-Exact Cycle,(More)
For many fixed-parameter problems that are trivially solvable in polynomial-time, such as k-Dominating Set, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as k-Feedback Vertex Set, exhibit fixed-parameter tractability: for each fixed k the problem is solvable in time bounded by a(More)
For many fixed-parameter problems that are trivially solvable in polynomial-time, such as kDOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as FEEDBACK VERTEX SET, exhibit fixed-parameter tractability: for each fixed k the problem is solvable in time bounded by a(More)
We describe new results in parameterized complexity theory. In particular, we prove a number of concrete hardness results for W [P ], the top level of the hardness hierarchy introduced by Downey and Fellows in a series of earlier papers. We also study the parameterized complexity of analogues of PSPACE via certain natural problems concerning k-move games.(More)
For many fixed-parameter problems that are trivially soluable in polynomial time, such as (k-)DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as (k-)FEEDBACK VERTEX SET, exhibit fixed-parameter tractability: for each fixed k the problem is soluable in time bounded by a(More)
One of the major efforts in molecular biology is the computation of phylogenies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time algorithms for a few special cases, and many relaxations of the(More)
Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it. Many applications of interval graphs also generalize to multiple-interval graphs, often allowing for more robustness in the modeling of the specific application. With this motivation in mind, a recent systematic(More)
The VERTEX COVER problem asks, for input consisting of a graph G on n vertices, and a positive integer k, whether there is a set of k vertices such that every edge of G is incident with at least one of these vertices. We give an algorithm for this problem that runs in time O(kn + (1.324718)‘k’). In particular, this gives an 0( ( 1.324718)“n2) algorithm to(More)