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.
4000197
Lot-sizing scheduling with batch setup times
This paper is concerned with scheduling independent jobs on m parallel machines in such a way that the makespan is minimized. Each job j is allowed to split arbitrarily into several parts, which can be individually processed on any machine at any time. However, a setup for uninterrupted sj time units is required before any split part of job j can be processed on any machine. The problem is strongly NP-hard if the number m of machines is variable and weakly NP-hard otherwise. We give a polynomial-time $$\frac{5}{3}$$-approximation algorithm for the former case and a fully polynomial-time approximation scheme for the latter.
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.
16166391
Linear k-arboricities on trees
Abstract For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number l such that the edge set E(G) can be partitioned into l disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)⩽m.
2373278
A discriminative HMM/N-gram-based retrieval approach for mandarin spoken documents
In recent years, statistical modeling approaches have steadily gained in popularity in the field of information retrieval. This article presents an HMM/N-gram-based retrieval approach for Mandarin spoken documents. The underlying characteristics and the various structures of this approach were extensively investigated and analyzed. The retrieval capabilities were verified by tests with word- and syllable-level indexing features and comparisons to the conventional vector-space model approach. To further improve the discrimination capabilities of the HMMs, both the expectation-maximization (EM) and minimum classification error (MCE) training algorithms were introduced in training. Fusion of information via indexing word- and syllable-level features was also investigated. The spoken document retrieval experiments were performed on the Topic Detection and Tracking Corpora (TDT-2 and TDT-3). Very encouraging retrieval performance was obtained.
38200007
Total colorings of equibipartite graphs
Abstract The total chromatic number χτ ( G ) of a graph G is the least number of colors needed to color the vertices and the edges of G such that no adjacent or incident pair of elements receive the same color. A simple graph G is called type 1 if χτ ( G ) = Δ ( G ) + 1, where Δ ( G ) is the maximum degree of G . In this paper we prove the following conjecture of Chen et al.: An ( n − 2)-regular equibipartite graph K n , n − E ( J ) is type 1 if and only if J contains a 4-cycle.
11015337
Composite subset measures
Measures are numeric summaries of a collection of data records produced by applying aggregation functions. Summarizing a collection of subsets of a large dataset, by computing a measure for each subset in the (typically, user-specified) collection is a fundamental problem. The multidimensional data model, which treats records as points in a space defined by dimension attributes, offers a natural space of data subsets to be considered as summarization candidates, and traditional SQL and OLAP constructs, such as GROUP BY and CUBE, allow us to compute measures for subsets drawn from this space. However, GROUP BY only allows us to summarize a limited collection of subsets, and CUBE summarizes all subsets in this space. Further, they restrict the measure used to summarize a data subset to be a one-step aggregation, using functions such as SUM, of field-values in the data records.In this paper, we introduce composite subset measures, computed by aggregating not only data records but also the measures of other related subsets. We allow summarization of naturally related regions in the multidimensional space, offering more flexibility than either GROUP BY or CUBE in the choice of what data subsets to summarize. Thus, our framework allows more meaningful summaries to be computed for a targeted collection of data subsets.We propose an algebra called AW-RA and an equivalent pictorial language called aggregation workflows. Aggregation workflows allow for intuitive expression of composite measure queries, and the underlying algebra is designed to facilitate efficient multiscan execution. We describe an evaluation framework based on multiple passes of sorting and scanning over the original dataset. In each pass, several measures are evaluated simultaneously, and dependencies between these measures and containment relationships between the underlying subsets of data are orchestrated to reduce the memory footprint of the computation. We present a performance evaluation that demonstrates the benefits of our approach.
14354011
A study of the total chromatic number of equibipartite graphs
Abstract The total chromatic number χ t ( G ) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibipartite graphs of order 2 n with maximum degree n − 1. As a part of our results, we disprove the biconformability conjecture.