15064123
A new proof of Melnikov's conjecture on the edge-face coloring of plane graphs
In 1975, Melnikov conjectured that the edges and faces of each plane graph G may be colored with Δ(G)+3 colors so that any two adjacent or incident elements receive different colors, where Δ(G) is the maximum degree of G. Two similar, yet independent, proofs of this conjecture have been published recently by Waller (J. Combin. Theory Ser. B 69 (1997) 219) and Sanders and Zhao (Combinatorica 17 (1997) 441). Both proofs made use of the Four-Color Theorem. This paper presents a new proof of Melnikov's conjecture independent of the Four-Color Theorem.
6853966
Total chromatic number of planar graphs with maximum degree ten
11186519
Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers
Let G be a graph of nonnegative characteristic and let g(G) and @D(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (1) @D(H)= =11; (2) @D(H)= =7; (3) @D(H)= =5 or G does not contain 4-cycles and 5-cycles; (4) @D(H)= =11; (2) col"g(G)= =7; (3) col"g(G)= =5 or G contains no 4-cycles and 5-cycles; (4) col"g(G)=<10 if G does not contain 4-cycles.
41218825
Relaxed game chromatic number of graphs
This paper discusses a coloring game on graphs. Let k, d be non-negative integers and C a set of k colors. Two persons, Alice and Bob, alternately color the vertices of G with colors from C, with Alice having the first move. A color i is legal for an uncolored vertex x if by coloring x with color i, the subgraph of G induced by those vertices of color i has maximum degree at most d. Each move of Alice or Bob colors an uncolored vertex with a legal color. The game is over if either all vertices are colored, or no more vertices can be colored with a legal color. Alice's goal is to produce a legal coloring which colors all the vertices of G, and Bob's goal is to prevent this from happening. We shall prove that if G is a forest, then for k = 3, d ≥ 1, Alice has a winning strategy. If G is an outerplanar graph, then for k = 6 and d ≥ 1, Alice has a winning strategy.
1003852
Upper Bounds of Entire Chromatic Number of Plane Graphs
The entire chromatic number χvef (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. Kronk and Mitchem (1973) conjectured that χvef (G) ≤ 1 + 4 for every plane graph G. In this paper we prove the conjecture for a plane graph G having χ ′(G) = 1 and give a upper bound χvef (G) ≤ 1+ 5 for all plane graphs, where χ ′(G) and 1 are the chromatic index and the maximum degree of G, respectively.
9810371
The edge-face choosability of plane graphs
A plane graph G is said to be k-edge-face choosable if, for every list L of colors satisfying |L(x)|=k for every edge and face x, there exists a coloring which assigns to each edge and each face a color from its list so that any adjacent or incident elements receive different colors. We prove that every plane graph G with maximum degree Δ(G) is (Δ(G)+3)-edge-face choosable.
3251955
Containment join size estimation: models and methods
Recent years witnessed an increasing interest in researches in XML, partly due to the fact that XML has now become the de facto standard for data interchange over the internet. A large amount of work has been reported on XML storage models and query processing techniques. However, few works have addressed issues of XML query optimization. In this paper, we report our study on one of the challenges in XML query optimization: containment join size estimation. Containment join is well accepted as an important operation in XML query processing. Estimating the size of its results is no doubt essential to generate efficient XML query processing plans. We propose two models, the interval model and the position model, and a set of estimation methods based on these two models. Comprehensive performance studies were conducted. The results not only demonstrate the advantages of our new algorithms over existing algorithms, but also provide valuable insights into the tradeoff among various parameters.
52828756
Fast computation of database operations using graphics processors
We present new algorithms for performing fast computation of several common database operations on commodity graphics processors. Specifically, we consider operations such as conjunctive selections, aggregations, and semi-linear queries, which are essential computational components of typical database, data warehousing, and data mining applications. While graphics processing units (GPUs) have been designed for fast display of geometric primitives, we utilize the inherent pipelining and parallelism, single instruction and multiple data (SIMD) capabilities, and vector processing functionality of GPUs, for evaluating boolean predicate combinations and semi-linear queries on attributes and executing database operations efficiently. Our algorithms take into account some of the limitations of the programming model of current GPUs and perform no data rearrangements. Our algorithms have been implemented on a programmable GPU (e.g. NVIDIA's GeForce FX 5900) and applied to databases consisting of up to a million records. We have compared their performance with an optimized implementation of CPU-based algorithms. Our experiments indicate that the graphics processor available on commodity computer systems is an effective co-processor for performing database operations.
11609470
Interpolating Polyhedral Models Using Intrinsic Shape Parameters
Metamorphosis, or morphing, is the gradual transformation of one shape into another. It generally consists of two subproblems: the correspondence problem and the interpolation problem. This paper presents a solution to the interpolation problem of transforming one polyhedral model into another. It is an extension of the intrinsic shape interpolation scheme (T. W. Sederberg, P. Gao, G. Wang and H. Mu, ‘2-D shape blending: an intrinsic solution to the vertex path problem, SIGGRAPH ’93, pp. 15–18.) for 2D polygons. Rather than considering a polyhedron as a set of independent points or faces, our solution treats a polyhedron as a graph representing the interrelations between faces. Intrinsic shape parameters, such as dihedral angles and edge lengths that interrelate the vertices and faces in the two graphs, are used for interpolation. This approach produces more satisfactory results than the linear or cubic curve paths would, and is translation and rotation invariant.  1997 by John Wiley & Sons, Ltd.
2987996
Mining patterns in long sequential data with noise
Pattern discovery in time series data has been a problem of great importance in many fields, e.g., computational biology, performance analysis, consumer behavior, etc. Recently, considerable amount of research has been carried out in this area. The facts that the input data is typically very large and noises may present in various formats pose great challenge to the mining process. Recently, we have made several new research advances in this area. In this paper, we present some of them. We will survey new models proposed to address different types of noises as well as scalable algorithms developed for efficiently mining patterns under each model.
62579240
A Selective Rendering Method for Data Visualization
Author(s): Wang, Wencheng; Wu, En-Hua; Max, Nelson | Abstract: Selective visualization is a solution for visualizing data of large size and dimensionality. In this paper a new method is proposed for effectively rendering certain chosen parts among the full set of data in terms of a colour buffer, referred to as the virtual plane, for storing intermediate results. By this method, scientists may concentrate their attention on the contents of data in which they are interested. Besides, the method could be easily integrated with all the current direct volume rendering techniques, especially progressive refinement methods and selective methods.