11584790
SLEVEs for planar spline curves
Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve.We develop general criteria, that certify correctness of a global, polygonal enclosure built from a sequence of individual bounding boxes by extending and intersecting their edges. These criteria prove correctness of the sleve construction.
16426940
An accurate error measure for adaptive subdivision surfaces
A tight estimate on the maximum distance between a subdivision surface and its linear approximation is introduced to guide adaptive subdivision with guaranteed accuracy.
43142618
Efficient Algorithms for k-Terminal Cuts on Planar Graphs
The minimum k-terminal cut problem is of considerable theoretical interest and arises in several applied areas such as parallel and distributed computing, VLSI circuit design, and networking. In this paper, we present two new approximation and exact algorithms for this problem on an n-vertex undirected weighted planar graph G. For the case when the k terminals are covered by the boundaries of m > 1 faces of G, we give a min{O(n2 log n log m), O(m2n1.5 log2 n+kn)} time algorithm with a (2 - 2/k)-approximation ratio (clearly, m ≤ k). For the case when all k terminals are covered by the boundary of one face of G, we give an O(nk3 +(n log n)k2) time exact algorithm, or a linear time exact algorithm if k = 3, for computing an optimal k-terminal cut. Our algorithms are based on interesting observations and improve the previous algorithms when they are applied to planar graphs.
2385106
The intensity level reduction in radiation therapy
In this paper, we study an interesting intensity level reduction (ILR) problem, which is crucial for solving the "step-and-shoot" delivery planning problem in Intensity-Modulated Radiation Therapy (IMRT). IMRT aims to deliver a highly conformal radiation dose to a target tumor while sparing the surrounding normal tissues. Effective intensity level reduction approaches significantly reduce the patient's exposure under the radiation and improve the treatment efficiency. We propose a new intensity level reduction method for step-and-shoot delivery planning, and further model the intensity level reduction problem as computing a set of shortest monotone paths (SMPs) in certain specific geometric graphs, called multi-column graphs, of pseudo-polynomial sizes. Based on a judicious characterization of the intrinsic geometric structures of the graphs, we develop a novel graph pruning scheme and compute the SMPs without explicitly constructing the graphs, yielding an efficient O(mn logn) time algorithm for solving the intensity level reduction problem on an intensity map (specifying a radiation dose prescription) of size m x n.
33348508
Knowledge Discovery in Multiple Databases
2809067
Support vector machines based on K-means clustering for real-time business intelligence systems
Support vector machines (SVM) have been applied to build classifiers, which can help users make well-informed business decisions. Despite their high generalisation accuracy, the response time of SVM classifiers is still a concern when applied into real-time business intelligence systems, such as stock market surveillance and network intrusion detection. This paper speeds up the response of SVM classifiers by reducing the number of support vectors. This is done by the K-means SVM (KMSVM) algorithm proposed in this paper. The KMSVM algorithm combines the K-means clustering technique with SVM and requires one more input parameter to be determined: the number of clusters. The criterion and strategy to determine the input parameters in the KMSVM algorithm are given in this paper. Experiments compare the KMSVM algorithm with SVM on real-world databases, and the results show that the KMSVM algorithm can speed up the response time of classifiers by both reducing support vectors and maintaining a similar testing accuracy to SVM.
42284012
Efficient Algorithms for k-Terminal Cuts on Planar Graphs
AbstractThe minimum k-terminal cut problem is of considerable theoretical interest and arises in several
applied areas such as parallel and distributed computing, VLSI circuit design, and networking. In this paper
we present two new approximation and exact algorithms for this problem on an n-vertex undirected weighted
planar graph G. For the case when the k terminals are covered by the boundaries of m > 1 faces of G, we
give a min{O(n2 log n logm), O(m2n1.5 log2n + kn)} time algorithm with a (2–2/k)-approximation ratio
(clearly, m \le k). For the case when all k terminals are covered by the boundary of one face of G, we give an
O(nk3 + (n log n)k2) time exact algorithm, or a linear time exact algorithm if k = 3, for computing an optimal
k-terminal cut. Our algorithms are based on interesting observations and improve the previous algorithms when
they are applied to planar graphs. To our best knowledge, no previous approximation algorithms specifically
for solving the k-terminal cut problem on planar graphs were known before. The (2–2/k)-approximation
algorithm of Dahlhaus et al. (for general graphs) takes O(kn2 log n) time when applied to planar graphs. Our
approximation algorithm for planar graphs runs faster than that of Dahlhaus et al. by at least an O(k/logm)
factor (m \le k).