16547141
Edge domination in complete partite graphs
Abstract An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D . An edge domatic partition of a graph G =( V , E ) is a collection of pairwise-disjoint edge dominating sets of G whose union is E . The maximum size of an edge domatic partition of G is called the edge domatic number . In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split graphs .
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.
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.
13073706
Graph homotopy and Graham homotopy
Abstract Simple-homotopy for cell complexes is a special type of topological homotopy constructed by elementary collapses and elementary expansions. In this paper, we introduce graph homotopy for graphs and Graham homotopy for hypergraphs and study the relation between the two homotopies and the simple-homotopy for cell complexes. The graph homotopy is useful to describe topological properties of discretized geometric figures, while the Graham homotopy is essential to characterize acyclic hypergraphs and acyclic relational database schemes.
7786721
Geometry completion and detail generation by texture synthesis
We present a novel method for patching holes in polygonal meshes and synthesizing surfaces with details based on existing geometry. The most novel feature of our proposed method is that we transform the 3D geometry synthesis problem into a 2D domain by parameterizing surfaces and solve this problem in that domain. We then derive local geometry gradient images that encode intrinsic local geometry properties, which are invariant to object translation and rotation. The 3D geometry of holes is then reconstructed from synthesized local gradient images. This method can be extended to execute other mesh editing operations such as geometry detail transfer or synthesis. The resulting major benefits of performing geometry synthesis in 2D are more flexible and robust control, better leveraging of the wealth of current 2D image completion methods, and greater efficiency.
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.
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.
10767971
The duality between information embedding and source coding with side information and some applications
Aspects of the duality between the information-embedding problem and the Wyner-Ziv (1976) problem of source coding with side information at the decoder are developed and used to establish a spectrum new results on these and related problems, with implications for a number of important applications. The single-letter characterization of the information-embedding problem is developed and related to the corresponding characterization of the Wyner-Ziv problem, both of which correspond to optimization of a common mutual information difference. Dual variables and dual Markov conditions are identified, along with the dual role of noise and distortion in the two problems. For a Gaussian context with quadratic distortion metric, a geometric interpretation of the duality is developed. From such insights, we develop a capacity-achieving information-embedding system based on nested lattices. We show the resulting encoder-decoder has precisely the same decoder-encoder structure as the corresponding Wyner-Ziv system based on nested lattices that achieves the rate-distortion limit. For a binary context with Hamming distortion metric, the information-embedding capacity is developed, along with its relationship to the corresponding Wyner-Ziv rate-distortion function. In turn, an information-embedding system for this case based on nested linear codes is constructed having an encoder-decoder that is identical to the decoder-encoder structure for the corresponding system that achieves the Wyner-Ziv rate-distortion limit. Finally, based on these results, a simple layered joint source-channel coding system is developed with a perfectly symmetric encoder-decoder structure. Its application and performance is discussed in a broadcast setting in which there is a need to control the fidelity experienced by different receivers. Among other results, we show that such systems and their multilayer extensions retain attractive optimality properties in the Gaussian-quadratic case, but not in the binary-Hamming case.