Catherine McCartin

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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)
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)
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)
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, ..., 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)
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)
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)