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We describe some new, simple and apparently general methods for designing FPT algorithms, and illustrate how these can be used to obtain a significantly improved FPT algorithm for the Maximum Leaf Spanning Tree problem. Furthermore, we sketch how the methods can be applied to a number of other well-known problems, including the para-metric dual of… (More)

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)

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)

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)

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 parame-terized approximation… (More)

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)

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,. .. , t k } 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… (More)

We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a… (More)

We present a novel approach to the analysis of dependency graphs of object-oriented programs. We propose to use the Girvan-Newman clustering algorithm to compute the modular structure of programs. This is useful in assisting software engineers to redraw component boundaries in software, in order to improve the level of reuse and maintainability. The results… (More)