590214
The Chromaticity of Certain Complete Multipartite Graphs
Abstract.In this paper, we first establish a useful inequality on the minimum real roots of the adjoint polynomials of the complete graphs. By using it, we investigate the chromatic uniqueness of certain complete multipartite graphs. An unsolved problem (i.e., Problem 11), posed by Koh and Teo in Graph and Combin. 6(1990) 259–285, is completely solved by giving it a positive answer. Moreover, many existing results on the chromatic uniqueness of complete multipartite graphs are generalized.
17735073
On problems and conjectures on adjointly equivalent graphs
For a graph G, let h(G,x) denote its adjoint polynomial and @b(G) denote the minimum real root of h(G,x). Two graphs H and G are said to be adjointly equivalent if h(H,x)=h(G,x). Let F"1={G|@b(G)>-4} and F"2={G|@b(G)>=-4}. In this paper, we give a necessary and sufficient condition for two graphs H and G in F"i to be adjointly equivalent, where i=1,2. We also solve some problems and conjectures proposed by Dong et al. (Discrete Math. 258 (2002) 303-321).
27925843
Chromaticity of a family of K4-homeomorphs
Abstract We discuss the chromaticity of one family of K 4 -homeomorphs which has exactly 2 adjacent paths of length 1, and give sufficient and necessary condition for the graphs in the family to be chromatically unique.
37263695
A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs
Let P(G,@l) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H,@l)=P(G,@l) implies [email protected]?G. Koh, Teo and Chia conjectured that for any integers n and k with n>=k+2>=4, the complete tripartite graph K(n-k,n,n) is chromatically unique. Let K(n,m,r)-S denote the graph obtained by deleting all edges in S from the complete tripartite K(n,m,r). In this paper, we establish that for any positive integer n>=m>=r>=2, the chromatic equivalence class of K(n,m,r) is contained in the family {K(x,y,z)-S|1==2k and k>=2.
5589315
Chromatic uniqueness of the complements of certain forests
Abstract A tree is called a tree of T -shape if its degree sequence is (1,1,1,2,2, …, 2,3). In this paper, we prove that the complement of the disjoint union of any number copies of a kind of tree of T -shape is chromatically unique by studying its adjoint polynomial.
44250435
An Adaptive Agent Society for Environmental Scanning through the Internet
Business managers need to promptly respond to environmental changes. Environmental scanners are thus important in discovering and monitoring the information of interest (IOI). In this paper, we explore continuous and resource-bounded environmental scanning (CRBES). The scanner continuously scans for new IOI without consuming too much resource (e.g. bandwidths of computer networks and services of information servers). In that case, new IOI may be discovered in a complete and timely manner without making the related networks and servers too exhausted to provide services. We develop a multiagent framework ACES to achieve CRBES. The agents form an adaptive society by adapting their population and specialty to information needs of individual users, resource limitation of environmental scanning, distribution of IOI in the environments, and update behaviors of the IOI. The delivery of ACES to businesses may constantly provide timelier IOI without causing serious problems to the Intranet and the Internet communities.
1875598
Segmentation of 3D meshes through spectral clustering
We formulate and apply spectral clustering to 3D mesh segmentation for the first time and report our preliminary findings. Given a set of mesh faces, an affinity matrix which encodes the likelihood of each pair of faces belonging to the same group is first constructed. Spectral methods then use selected eigenvectors of the affinity matrix or its closely related graph Laplacian to obtain data representations that can be more easily clustered. We develop an algorithm that favors segmentation along concave regions, which is inspired by human perception. Our algorithm is theoretically sound, efficient, simple to implement, andean achieve high-quality segmentation results on 3D meshes.
42113272
Dynamic Category Profiling for Text Filtering and Classification
Information is often represented in text form and classified into categories for efficient browsing, retrieval, and dissemination. Unfortunately, automatic classifiers may conduct many misclassifications. One of the reasons is that the documents for training the classifiers are mainly from the categories, leading the classifiers to derive category profiles for distinguishing each category from others, rather than measuring the extent to which a document's content overlaps that of a category. To tackle the problem, we present a technique DP4FC to help various classifiers to improve the mining of category profiles. Upon receiving a document, DP4FC helps to create dynamic category profiles with respect to the document, and accordingly helps to make proper filtering and classification decisions. Theoretical analysis and empirical results show that DP4FC may make a classifier's performance both better and more stable.
40972997
Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks
Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is developed. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.
43626831
Parsing-Driven Generalization for Natural Language Acquisition
Parsing is an important step in natural language processing. It involves tasks of searching for applicable grammatical rules which can transform natural language sentences into their corresponding parse trees. Therefore parsing can be viewed as problem solving, and language acquisition can be achieved by generalizing problem solving heuristics. In this paper we investigate how machine learning methodologies can be integrated with a Wait-And-See Parser (the problem solver) to acquire parsing-related knowledge that is needed for the parser. We call this approach parsing-driven generalization since learning (acquisition of parsing rules and classification of lexicons) is basically derived from the parsing process. Three types of generalization are reported in this paper: simple generalization, generalization by asking questions, and generalization back-propagation. Simple generalization generalizes any two parsing rules whose action parts (right-hand sides) are the same but whose condition parts (left-hand sides) have a single difference. Generalization by asking questions is triggered when a “climbing-up” move on a concept hierarchy is attempted. It is necessary for avoiding over-generalization. Generalization back-propagation propagates a confirmed generalization of some later parsing rule back to its precedent rules in a parsing sequence and thus causes them to be generalized as well. It can reduce the number of questions asked by the system. With these three types of generalization and a mechanism for maintaining lexicon classification (the domain concept hierarchy), parsing and learning can interact to utilize and acquire parsing-related knowledge. To promote the practical performance of parsing after learning, a relaxation parsing mechanism is also designed to process unseen sentences.