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- Rodney G. Downey, Michael R. Fellows, Catherine McCartin
- IWPEC
- 2006

Parameterized complexity is fast becoming accepted as an important strand in the mainstream of algorithm design and analysis. Up until now, most of the work in the area has focussed on exact algorithms for decision problems. The goal of the present paper is to apply parameterized ideas to approximation. We begin exploration of parameterized approximation… (More)

- Rodney G. Downey, Michael R. Fellows, Catherine McCartin, Frances A. Rosamond
- Inf. Process. Lett.
- 2008

A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no k-Dominating Set, or (2) produces a dominating set of size at most g(k), where g(k) is some fixed function of k. Such an outcome is termed an FPT approximation algorithm. We describe some results that begin to provide… (More)

- Magnus Bordewich, Catherine McCartin, Charles Semple
- J. Discrete Algorithms
- 2008

In this paper, we give a (polynomial-time) 3-approximation algorithm for the rooted subtree prune and regraft distance between two phylogenetic trees. This problem is known to be NP-complete and the best previously known approximation algorithm is a 5-approximation. We also give a faster fixed-parameter algorithm for the rooted subtree prune and regraft… (More)

- Callum Lowcay, Stephen R. Marsland, Catherine McCartin
- SITIS
- 2013

- Catherine McCartin
- Ann. Pure Appl. Logic
- 2002

Parameterized complexity has so far been largely con ned to consideration of computational problems as decision or search prob lems However it is becoming evident that the parameterized point of view can lead to new insight into counting problems The goal of this article is to introduce a formal framework in which one may consider parameterized counting… (More)

- Michael Hallett, Matthew Kitching, +7 authors David R. Wood
- 2001

A bipartite graph is biplanar if the vertices can be placed on two parallel lines (layers) in the plane such that there are no edge crossings when edges are drawn as line segments between the layers. In this paper we study the 2-Layer Planarization problem: can k edges be deleted from a given graph G so that the remaining graph is biplanar? This problem is… (More)

- Michael T. Hallett, Catherine McCartin
- Theory of Computing Systems
- 2007

Given two unrooted, binary trees, T1 and T2, leaf labelled bijectively by a set of species L, the Maximum Agreement Forest (MAF) problem asks to find a minimum cardinality collection F = {t1, ..., tk} of phylogenetic trees where each element of F is a subtree of both T1 and T2, the elements of F are pairwise disjoint, and the leaf labels for the elements of… (More)

- Michael R. Fellows, Catherine McCartin
- Theor. Comput. Sci.
- 2003

Given a set T of tasks, each of unit length and having an individual deadline d(t)∈ Z, a set of precedence constraints on T , and a positive integer k6 |T |, we can ask “Is there a one-processor schedule for T that obeys the precedence constraints and contains no more than k late tasks?” This is a well-known NP-complete problem. We might also inquire “Is… (More)

- Rodney G. Downey, Catherine McCartin
- Developments in Language Theory
- 2004

Recently there have been some new initiatives in the field of parameterized complexity. In this paper, we will report on some of these, concentrating on some open questions, and also looking at some of our ideas towards applying ideas of parametric complexity in the field of online model theory.

- Vida Dujmovic, Michael R. Fellows, +9 authors David R. Wood
- Algorithmica
- 2001

A bipartite graph is biplanar if the vertices can be placed on two parallel lines (layers) in the plane such that there are no edge crossings when edges are drawn as line segments between the layers. In this paper we study the 2-Layer Planarization problem: Can k edges be deleted from a given graph G so that the remaining graph is biplanar? This problem is… (More)