29901411
Bin Packing and Covering Problems with Rejection
In this paper we consider the following problems: We are given a set of n items {u1, i¾?, un}, each item ui is characterized by its size wi∈ 0,1] and its penalty/profit pii¾? 0, and a number of unit-capacity bins. An item can be either rejected, in which case we pay/get its penalty/profit, or put into one bin under the constraint that the total size of the items in the bin is not greater/smaller than 1. No item can be spread into more than one bin. The objective is to minimize/maximize the sum of the number of used/covered bins and the penalties/profits of all rejected items. We call the problems bin packing/covering with rejection penalties/profits, and denoted by BPR and BCR respectively. For the online BPR problem, we present an algorithm with an absolute competitive ratio of 2.618 while the lower bound is 2.343, and an algorithm with an asymptotic competitive ratio of arbitrarily close to 7/4 while the lower bound is 1.540. For the offline BPR problem, we present an algorithm with an absolute worst-case ratio of 2 while the lower bound is 3/2, and an algorithm with an asymptotic worst-case ratio of 3/2. For the online BCR problem, we show that no algorithm can have an absolute competitive ratio of greater than 0, and present an algorithm with an asymptotic competitive ratio of 1/2, which is the best possible. For the offline BCR problem, we also present an algorithm with an absolute worst-case ratio of 1/2 which matches the lower bound.
15248292
Preemptive online algorithms for scheduling with machine cost
Abstract.For most scheduling problems the set of machines is fixed initially and remains unchanged. Recently Imreh and Noga proposed adding the concept of machine cost to scheduling problems and considered the so-called List Model problem. For this problem, we are given a sequence of independent jobs with positive sizes, which must be processed non-preemptively on a machine. No machines are initially provided, and when a job is revealed the algorithm has the option to purchase new machines. The objective is to minimize the sum of the makespan and cost of machines. In this paper, a modified model of List Model is presented where preemption is allowed. For this model, it is shown that better performance is possible. We present an online algorithm with a competitive ratio of $(2\sqrt{6} + 2)/5\approx 1.3798$ while the lower bound is 4/3. For the semi-online problem with decreasing sizes, we design an optimal algorithm with a competitive ratio of 4/3, which improves the known upper bound of 3/2. The algorithm does not introduce any preemption, and hence is also an optimal semi-online algorithm for the non-preemptive semi-online problem. For the semi-online problem with known largest size, we present an optimal algorithm with a competitive ratio of 4/3.
11744887
Harmonic volumetric mapping for solid modeling applications
Harmonic volumetric mapping for two solid objects establishes a one-to-one smooth correspondence between them. It finds its applications in shape registration and analysis, shape retrieval, information reuse, and material/texture transplant. In sharp contrast to harmonic surface mapping techniques, little research has been conducted for designing volumetric mapping algorithms due to its technical challenges. In this paper, we develop an automatic and effective algorithm for computing harmonic volumetric mapping between two models of the same topology. Given a boundary mapping between two models, the volumetric (interior) mapping is derived by solving a linear system constructed from a boundary method called the fundamental solution method. The mapping is represented as a set of points with different weights in the vicinity of the solid boundary. In a nutshell, our algorithm is a true meshless method (with no need of specific connectivity) and the behavior of the interior region is directly determined by the boundary. These two properties help improve the computational efficiency and robustness. Therefore, our algorithm can be applied to massive volume data sets with various geometric primitives and topological types. We demonstrate the utility and efficacy of our algorithm in shape registration, information reuse, deformation sequence analysis, tetrahedral remeshing and solid texture synthesis.
15418267
Incorporating Rigid Structures in Non-rigid Registration Using Triangular B-Splines
For non-rigid registration, the objects in medical images are usually treated as a single deformable body with homogeneous stiffness distribution. However, this assumption is invalid for certain parts of the human body, where bony structures move rigidly, while the others may deform. In this paper, we introduce a novel registration technique that models local rigidity of pre-identified rigid structures as well as global non-rigidity in the transformation field using triangular B-splines. In contrast to the conventional registration method based on tensor-product B-splines, our approach recovers local rigid transformation with fewer degrees of freedom (DOFs), and accurately simulates sharp features (C0 continuity) along the interface between deformable regions and rigid structures, because of the unique advantages offered by triangular B-splines, such as flexible triangular domain, local control and space-varying smoothness modeling. The accurate matching of the source image with the target one is accomplished through the use of a variational framework, in which a composite energy, measuring the image dissimilarity and enforcing local rigidity and global smoothness, is minimized subject to pre-defined point-based constraints. The algorithm is tested on both synthetic and real 2D images for its applicability. The experimental results show that, by accurately modeling sharp features using triangular B-splines, the deformable regions in the vicinity of rigid structures are less constrained by the global smoothness regularization and therefore contribute extra flexibility to the optimization process. Consequently, the registration quality is improved considerably.
45341657
3-D Reconstruction of Macroscopic Optical Brain Slice Images
We present a method for reconstruction of macroscopic optical images of post-mortem brain slices to form a 3-D volume. This forms a key part of a series of procedures to allow post mortem findings to be accurately registered with MR images, and more generally provides a method for 3-D mapping of the distribution of pathological changes throughout the brain. In this preliminary work, four brains from a study of Creutzfeldt-Jakob disease were examined. After brain fixation, the pathologist cut coronal slices several mm thick through the brain. The anterior and posterior faces of each slice were photographed. We show that the 2-D co-registration of each such pair of images was most effectively obtained if the slice was placed in a jig before photographing. Fiducials on the jig were detected automatically and point-based rigid registration computed. For co-registration between slices, i.e., across a single cut, an intensity-based method for 2-D non-rigid registration is used which provided satisfactory results. By propagating the 2-D registrations through the volume and using the known slice thickness, the 3-D volume was reconstructed.
28965598
A semantic matchmaker service on the grid
A fundamental task on the Grid is to decide what jobs to run on what computing resources based on job or application requirements. Our previous work on ontology-based matchmaking discusses a resource matchmaking mechanism using Semantic Web technologies. We extend our previous work to provide dynamic access to such matchmaking capability by building a persistent online matchmaking service. Our implementation uses the Globus Toolkit for the Grid service development, and exploits the monitoring and discovery service in the Grid infrastructure to dynamically discover and update resource information. We describe the architecture of our semantic matchmaker service in the poster.
8614411
Manifold T-Spline
This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offering a natural mechanism for generalizing the tensor-product splines throughout the entire manifold. In our shape modeling framework, the manifold T-splines are globally well-defined except at a finite number of extraordinary points, without the need of any tedious trimming and patching work. We present an efficient algorithm to convert triangular meshes to manifold T-splines. Because of the natural, built-in hierarchy of T-splines, we can easily reconstruct a manifold T-spline surface of high-quality with LOD control and hierarchical structure.