11520313
Linear Vertex Arboricity, Independence Number and Clique Cover Number
The linear vertex-arboricity of a graph G is defined to the minimum number of subsets into which the vertex-set G can be partitioned so that every subset induces a linear forest. In this paper, we give the upper and lower bounds for sum and product of linear vertex-arboricity with independence number and with clique cover number respectively. All of these bounds are sharp.
38207892
On the Relations Between Arboricity and Independent Number Or Covering Number
In this paper, the following results are obtained: a(G) + β(G) ⩽ p + 1, ⌈p2⌉ ⩽ a(G)β(G), ⌈p2⌉ ⩽ a′(G) + gb′(G) ⩽ pa′(G) + α′(G) ⩽ 2⌈p2⌉ (δ ⩽ 1) and all bounds are sharp, where p = ¦V(G)¦, ⌈x⌉ denotes the smallest integer greater than or equal to x, a(G) is the vertex arboricity, a′(G) is the edge arboricity, α′(G) is the edge covering number, β(G) is the vertex independent number, β′(G) is the edge independent number, and δ is the minimum degree of G.
24192218
On point-linear arboricity of planar graphs
The point-linear arboricity of a graph G=(V, E), written as p 0 (G), is defined as p 0 (G)=min{k | there exists a partition of V into k subsets, V=∪=1 V i such that (V i ) is a linear forest for 1 >i>k}. In this paper, we will discuss the point-linear arboricity of planar graphs and obtained following results: p 0 (G)=2 if G is a outplanar graph. p 0 (G)=4 if G is a planar graph.
39858986
On the Connectivity of (4;g)-Cages
37643061
Adjacent strong edge coloring of graphs
Abstract For a graph G ( V , E ), if a proper k -edge coloring ƒ is satisfied with C ( u ) ≠ C ( v ) for uv ∈ E ( G ), where C(u) = {ƒ(uv) | uv ∈ E} , then ƒ is called k-adjacent strong edge coloring of G , is abbreviated k-ASEC , and χ ′ as ( G ) = min { k | k - ASEC of G } is called the adjacent strong edge chromatic number of G . In this paper, we discuss some properties of χ′ as ( G ), and obtain the χ′ as ( G ) of some special graphs and present a conjecture: if G are graphs whose order of each component is at least six, then χ ′ as ( G ) ≤ Δ ( G ) + 2, where Δ( G ) is the maximum degree of G .
45865876
Graph theoretic characterization and reliability of the generalized Boolean n-cube network
In this paper, a general class of Boolean n-cube structures is investigated. The interconnection is based on a mixed radix number system which results in a variety of generalized Boolean n-cube structures for a given number of processors N = x·2y, where x and y are positive integers. A number of interesting properties of the network are revealed. By a constructive method, the node connectivity of this network is found. Finally, we show that the graph is super-λ and is an optimal reliable structure for interconnection networks.
5318094
Fast approximation of centrality
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1 + ∈) factor in near-linear time.
17604851
Efficient point coverage in wireless sensor networks
We study minimum-cost sensor placement on a bounded 3D sensing field, R, which comprises a number of discrete points that may or may not be grid points. Suppose we have ℓ types of sensors available with different sensing ranges and different costs. We want to find, given an integer σ ≥ 1, a selection of sensors and a subset of points to place these sensors such that every point in R is covered by at least σ sensors and the total cost of the sensors is minimum. This problem is known to be NP-hard. Let ki denote the maximum number of points that can be covered by a sensor of the ith type. We present in this paper a polynomial-time approximation algorithm for this problem with a proven approximation ratio $${\gamma = \sum_{i=1}^{\ell} k_{i} -\sigma+1}$$. In applications where the distance of any two points has a fixed positive lower bound, each ki is a constant, and so we have a polynomial-time approximation algorithms with a constant guarantee. While γ may be large, we note that it is only a worst-case upper bound. In practice the actual approximation ratio is small, even on randomly generated points that do not have a fixed positive minimum distance between them. We provide a number of numerical results for comparing approximation solutions and optimal solutions, and show that the actual approximation ratios in these examples are all less than 3, even though γ is substantially larger.
14843520
Deriving knowledge from figures for digital libraries
Figures in digital documents contain important information. Current digital libraries do not summarize and index information available within figures for document retrieval. We present our system on automatic categorization of figures and extraction of data from 2-D plots. A machine-learning based method is used to categorize figures into a set of predefined types based on image features. An automated algorithm is designed to extract data values from solid line curves in 2-D plots. The semantic type of figures and extracted data values from 2-D plots can be integrated with textual information within documents to provide more effective document retrieval services for digital library users. Experimental evaluation has demonstrated that our system can produce results suitable for real-world use.
14507980
Effects of term segmentation on Chinese/English cross-language information retrieval
The majority of recent Cross-Language Information Retrieval (CLIR) research has focused on European languages. CLIR problems that involve East Asian languages such as Chinese introduce additional challenges, because written Chinese texts lack boundaries between terms. The paper examines three Chinese segmentation techniques in combination with two variants of dictionary-based Chinese to English query translation. The results indicate that failure to segment terms, particularly technical terms and names, can have a cascading effect that reduces retrieval effectiveness. Task-tuned segmentation algorithms and alternative term weighting strategies are suggested as productive directions for future work.