39846081
On-Line Algorithms for Cardinality Constrained Bin Packing Problems
The bin packing problem asks for a packing of a list of items from [0, 1] into the smallest possible number of bins having unit capacity. The k-item bin packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two efficient approximation algorithms for the on-line version of this problem. We show that, for increasing values of k, the asymptotic worst-case performance ratio of the first algorithm tends towards 2 and that the second algorithm has an asymptotic worst-case performance ratio of 2. Both heuristics considerably improve upon the best known result 2.7 of Krause, Shen and Schwetman. Moreover, we present algorithms for k = 2 and k = 3, where the result for k = 2 is best possible.
3992681
A Lower Bound for Randomized On-Line Scheduling Algorithms
We prove that any randomized algorithm for on-line scheduling jobs on m identical parallel machines must have a worst case ratio at least mm/(mm−(m−1)m) for every m, which tends to e/(e−1) ≈ 1.58 as m→∞. This ans wers a question posed in a recent paper by Bartal, Fiat, Karloff and Vohra.
4020261
On-Line Scheduling a Batch Processing System to Minimize Total Weighted Job Completion Time
Scheduling a batch processing system has been extensively studied in the last decade. A batch processing system is modelled as a machine that can process up to b jobs simultaneously as a batch. The scheduling problem involves assigning all n jobs to batches and determining the batch sequence in such a way that certain objective function of job completion times Cj is minimized. In this paper, we address the scheduling problem under the on-line setting in the sense that we construct our schedule irrevocably as time proceeds and do not know of the existence of any job that may arrive later. Our objective is to minimize the total weighted completion time ∑wjCj. We provide a linear time on-line algorithm for the unrestrictive model (i.e., b ≥ n) and show that the algorithm is 10/3-competitive. For the restrictive model (i.e., b < n), we first consider the (off-line) problem of finding a maximum independent vertex set in an interval graph with cost constraint (MISCP), which is NP-hard. We give a dual fully polynomial time approximation scheme for MISCP, which leads us to a (4 + ∈)-competitive on-line algorithm for any ∈ > 0 for the original on-line scheduling problem. These two on-line algorithms are the first deterministic algorithms of constant performance guarantees.
17041567
On-line scheduling of small open shops
We investigate the problem of on-line scheduling open shops of two and three machines with an objective of minimizing the schedule makespan. We first propose a 1.848-competitive permutation algorithm for the non-preemptive scheduling problem of two machines and show that no permutation algorithm can be better than 1.754-competitive. Secondly, we develop a (27/19)-competitive algorithm for the preemptive scheduling problem of three machines, which is most competitive.
4025640
Algorithms for on-line bin-packing problems with cardinality constraints
The bin-packing problem asks for a packing of a list of items of sizes from (0,1] into the smallest possible number of bins having unit capacity. The k-item bin-packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two efficient on-line algorithms for this problem. We show that, for increasing values of k, the bound on the asymptotic worst-case performance ratio of the first algorithm tends towards 2 and that the second algorithm has a ratio of 2. Both algorithms considerably improve upon the best known result of an algorithm, which has an asymptotic bound of 2.7 on its ratio. Moreover, we improve known bounds for all values of k by presenting on-line algorithms for k = 2 and 3 with bounds on their ratios close to optimal.
4000958
A Better Heuristic for Preemptive Parallel Machine Scheduling with Batch Setup Times
This paper addresses the problem of scheduling N jobs on M identical parallel machines with the objective of minimizing the makespan. Jobs are divided into B batches. A sequence-independent batch setup time on a machine is incurred whenever the machine starts its processing on or switches it from a job in one batch to a job in another batch. On the basis of a heuristic for this NP-hard problem proposed by Monma and Potts, a modified heuristic that requires the same implementing time $O(N + (M + B)\log (M + B))$ and is asymptotically optimal is presented. Furthermore, for a certain class of problems, which includes the case in which each batch contains a single job, it has the worst-case performance ratio $\tau _M = \max \{ {\frac{{3M}}{{2M + 1}},\frac{{3M - 4}}{{2M - 2}}} \}$.
10910603
Hybrid Forward Resampling and Volume Rendering
The transforming and rendering of discrete objects, such as traditional images (with or without depths) and volumes, can be considered as resampling problem – objects are reconstructed, transformed, filtered, and finally sampled on the screen grids. In resampling practices, discrete samples (pixels, voxels) can be considered either as infinitesimal sample points (simply called points) or samples of a certain size (splats). Resampling can also be done either forwards or backwards in either the source domain or the target domain. In this paper, we present a framework that features hybrid forward resampling for discrete rendering. Specifically, we apply this framework to enhance volumetric splatting. In this approach, minified voxels are taken simply as points filtered in screen space; while magnified voxels are taken as spherical splats. In addition, we develop two techniques for performing accurate and efficient perspective splatting. The first one is to efficiently compute the 2D elliptical geometry of perspectively projected splats; the second one is to achieve accurate perspective reconstruction filter. The results of our experiments demonstrate both the effectiveness of antialiasing and the efficiency of rendering using this
42366271
A Note on the m-Bounded Chromatic Number of a Tree
Abstract The m-bounded chromatic number of a graph G is the smallest number of colors required for a proper coloring of G in which each color is used at most m times. We will establish an exact formula for the m -bounded chromatic number of a tree.
11577696
A maximum-entropy chinese parser augmented by transformation-based learning
Parsing, the task of identifying syntactic components, e.g., noun and verb phrases, in a sentence, is one of the fundamental tasks in natural language processing. Many natural language applications such as spoken-language understanding, machine translation, and information extraction, would benefit from, or even require, high accuracy parsing as a preprocessing step.
 Even though most state-of-the-art statistical parsers were initially constructed for parsing in English, most of them are not language-specific, in that they do not rely on properties of the language that are specific to English. Therefore, construction of a parser in a given language becomes a matter of retraining the statistical parameters with a Treebank in the corresponding language.
 The development of the Chinese treebank [Xia et al. 2000] spurred the construction of parsers for Chinese. However, Chinese as a language poses some unique problems for the development of a statistical parser, the most apparent being word segmentation. Since words in written Chinese are not delimited in the same way as in Western languages, the first problem that needs to be solved before an existing statistical method can be applied to Chinese is to identify the word boundaries. This is a step that is neglected by most pre-existing Chinese parsers, which assume that the input data has already been pre-segmented.
 This article describes a character-based statistical parser, which gives the best performance to-date on the Chinese treebank data. We augment an existing maximum entropy parser with transformation-based learning, creating a parser that can operate at the character level. We present experiments that show that our parser achieves results that are close to those achievable under perfect word segmentation conditions.
16592812
A web-based virtual laboratory on a frequency modulation experiment
With the rapid proliferation of Internet technologies, accessing and operating engineering instruments remotely anytime anywhere is fast becoming a reality. This paper presents a new Web-based virtual laboratory on a frequency modulation experiment for the teaching of an undergraduate course on communication principles in the National University of Singapore (NUS). The laboratory requires only a common Web browser to access and incorporate schemes for reducing data traffic and authenticating users. It enables students to have a natural hands-on experience of using an expensive spectrum analyzer on a one-to-one basis and provides a solution for distant engineering education. The system uses a double client-server structure where access to the experiment is via two rounds of client-server processing. The virtual laboratory can be accessed at the Web site http://vlab.ee.nus.edu.sg/vlab/freqmod/index.html.
42441601
Hamiltonian uniform subset graphs
The uniform subset graph G(n, k, t) is defined to have all k-subsets of an n-set as vertices and edges joining k-subsets intersecting at t elements. We conjecture that G(n, k, t) is hamiltonian when it is different from the Petersen graph and does possess cycles. We verify this conjecture for k − t = 1, 2, 3 and for suitably large n when t = 0, 1.