We present data structures for maintaining the relative convex hull of a set of points (sites) in the presence of pairwise non-crossing line segments (barriers) that subdivide a bounding box into simply connected faces. Our data structures have O((n + m) log n) size for n sites and m barriers. They support O(m) barrier insertions and O(n) site deletions in O((m + n) polylog (mn)) total time, an...

The greedy triangulation of a nite planar point set is obtained by repeatedly inserting a shortest diagonal that doesn't intersect those already in the plane. We show that the problem of constructing the greedy triangulation of a nite set of points with integer coordinates in the plane is P-complete. This is the rst known geometric P-complete problem where the input is given as a set of points....

We introduce a framework for the construction, maintenance, and manipulation of arrangements of curves embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The framework applies to planes, cylinders, spheres, tori, and surfaces homeomorphic to them. We reduce the effort needed to generalize existing algorithms, such as the sweep line and zone traversal ...

This paper investigates the application of the Red-Black Half-Sweep Gauss-Seidel (HSGS-RB) method by using the half-sweep triangle finite element approximation equation based on the Galerkin scheme to solve two-dimensional Poisson equations. Formulations of the full-sweep and half-sweep triangle finite element approaches in using this scheme are also derived. Some numerical experiments are cond...

We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to them. A major goal of our work is to maximize code reuse by generalizing the prevalent sweep-line paradigm and its implementation so that it can be employed on a large class of surfaces and curves embedded on...

1 Introduction

We consider the problem of transposition and time-warp invariant (TTWI) polyphonic content-based music retrieval (CBMR) in symbolically encoded music. For this setting, we introduce two new algorithms based on dynamic programming. Given a query point set, of sizem, to be searched for in a database point set, of size n, and applying a search window of width w, our algorithms run in time O(mnw) f...

The problem of matching sets of points or sets of horizontal line segments in plane under translations is considered. For finding the exact occurrences of a point set of size m within another point set of size n we give an algorithm with running time O(mn), and for finding partial occurrences an algorithm with running time O(mn logm). To find the largest overlap between two line segment pattern...