23067524
A new method for proving chromatic uniqueness of graphs
Abstract We give a brief survey on a new method for proving the chromatic uniqueness of graphs by their adjoint polynomials. We obtain some simpler proofs of relevant theorems and a new family of chromatically unique graphs.
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.
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.
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.
10425168
Adjoint polynomials and chromatically unique graphs
Abstract The aim of this expository paper is to give a survey of the results on chromatically unique graphs obtained by studying their adjoint polynomials.
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).
7031488
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 textbf 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 bf 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 obtained. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.
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.
1352172
Spectral Sequencing Based on Graph Distance
The construction of linear mesh layouts has found various applications, such as implicit mesh filtering and mesh streaming, where a variety of layout quality criteria, e.g., span and width, can be considered. While spectral sequencing, derived from the Fiedler vector, is one of the best-known heuristics for minimizing width, it does not perform as well as the Cuthill-Mckee (CM) scheme in terms of span. In this paper, we treat optimal mesh layout generation as a problem of preserving graph distances and propose to use the subdominant eigenvector of a kernel (affinity) matrix for sequencing. Despite the non-sparsity of the affinity operators we use, the layouts can be computed efficiently for large meshes through subsampling and eigenvector extrapolation. Our experiments show that the new sequences obtained outperform those derived from the Fiedler vector, in terms of spans, and those obtained from CM, in terms of widths and other important quality criteria. Therefore, in applications where several such quality criteria can influence algorithm performance simultaneously, e.g., mesh streaming and implicit mesh filtering, the new mesh layouts could potentially provide a better trade-off.
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.
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.