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Abstract: The measure and conquer approach has proven to be a powerful tool to analyse exact algorithms for combinatorial problems like Dominating Set and Independent Set. This approach is used in this paper to obtain a faster exact algorithm for Dominating Set. We obtain this algorithm by considering a series of branch and reduce algorithms. This series is the result of an iterative process in which a mathematical analysis of an algorithm in the series with measure and conquer results in a convex or quasiconvex programming problem. The solution, by means of a computer, to this problem not only gives a bound on the running time of the algorithm, but can also give an indication on where to look for a new reduction rule, often giving a new, possibly faster algorithm. As a result, we obtain an time and polynomial space algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, a feature-preserving mesh hole-filling algorithm is realized by the polynomial blending technique. We first search for feature points in the neighborhood of the hole. These feature points allow us to define the feature curves with missing parts in the hole. A polynomial blending curve is constructed to complete the missing parts of the feature curves. These feature curves divide the original complex hole into small simple sub-holes. We use the Bézier–Lagrange hybrid patch to fill each sub-hole. The experimental results show that our mesh hole-filling algorithm can effectively restore the original shape of the hole. [Copyright &y& Elsevier]

Abstract: The problem of identifying the topology implied by wireframe drawings of polyhedral objects requires the identification of face loops, loops of edges which correspond to a face in the object the drawing portrays. In this paper, we survey the advantages and limitations of known approaches, and present and discuss test results which illustrate the successes and failures of a currently popular approach based on Dijkstra’s Algorithm. We conclude that the root cause of many failure cases is that the underlying algorithm assumes that the cost of traversing an edge is fixed. We propose a new polynomial-order algorithm for finding faces in wireframes. This algorithm could be adapted to any graph-theoretical least-cost circuit problem where the cost of traversing an edge is not fixed but context-dependent. [Copyright &y& Elsevier]