Matthew Kitching

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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)
We present a new probabilistic framework for finding likely variable assignments in difficult constraint satisfaction problems. Finding such assignments is key to efficient search, but practical efforts have largely been limited to random guessing and heuristically designed weighting systems. In contrast, we derive a new version of Belief Propagation (BP)(More)
Branch and bound is an effective technique for solving constraint optimization problems (COP’s). However, its search space expands very rapidly as the domain sizes of the problem variables grow. In this paper, we present an algorithm that clusters the values of a variable’s domain into sets. Branch and bound can then branch on these sets of values rather(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)
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)
OBJECTIVE To gain an insight into patients' perceptions and experiences of larval therapy. METHOD A phenomenological approach was adopted in which six patients who recently had had larval therapy were interviewed using an open, unstructured approach in two hospital settings. Data analysis was loosely based on Colaizzi's structured analysis technique. (More)
Caching, symmetries, and search with decomposition are powerful techniques for pruning the search space of constraint problems. In this paper we present an innovative way of efficiently combining these techniques with branch and bound for solving certain types of constraint optimization problems (COPs). Our new method significantly reduces the overhead of(More)
We consider the following graph embedding question: given a graph G, is it possible to map its vertices to points in 3D such that G is isomorphic to the mutual nearest neighbor graph of the set P of points to which the vertices are mapped? We show that this problem is NP-hard. We do this by extending the “logic engine” method to three dimensions by using(More)
Decomposition is an effective technique for solving discrete Constraint Optimization Problems (COPs) with low tree-width. On problems with high treewidth, however, existing decomposition algorithms offer little advantage over branch and bound search (B&B). In this paper we propose a method for exploiting decomposition on problems with high treewidth. Our(More)