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.
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.
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.
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).
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.
884902
CLTC: a cluster-based topology control for ad hoc networks
The topology of an ad hoc network has a significant impact on its performance in that a dense topology may induce high interference and low capacity, while a sparse topology is vulnerable to link failure and network partitioning. Topology control aims to maintain a topology that optimizes network performance while minimizing energy consumption. Existing topology control algorithms utilize either a purely centralized or a purely distributed approach. A centralized approach, although able to achieve strong connectivity (k-connectivity for k /spl ges/ 2), suffers from scalability problems. In contrast, a distributed approach, although scalable, lacks strong connectivity guarantees. We propose a hybrid topology control framework, cluster-based topology control (CLTC) that achieves both scalability and strong connectivity. By varying the algorithms utilized in each of the three phases of the framework, a variety of optimization objectives and topological properties can be achieved. In this paper, we present the CLTC framework; describe topology control algorithms based on CLTC and prove that k-connectivity is achieved using those algorithms; analyze the message complexity of an implementation of CLTC, namely, CLTC-A, and present simulation studies that evaluate the effectiveness of CLTC-A for a range of networks.
30610002
INQUIRY-BOUNDED MINING OF IMPRECISE DATA FOR ADAPTIVE INFORMATION MONITORING
Information monitoring (IM) is an essential activity for management and control. Generally speaking, an IM system aims to continuously check for information updates. Once an update is detected, it triggers suitable actions such as exception validation, exception handling, and user notification. Since information sources (e.g., individual persons and servers) often cannot notify the IM system of updates, the IM system needs to actively inquire about the current status of the items being monitored. However, data inquiry may be costly, and uncontrolled inquiry may even exhaust the information sources. IM should thus be conducted under an inquiry-bounded constraint (i.e., limiting the number of inquiries). Under such a constraint, an IM system should inquire the right targets at the right time by adapting to the update behavior (i.e., rough update frequency at each time period) of each information item. This requirement brings a significant challenge to the design of the IM system: mining the imprecise data that is sampled in an inquiry-bounded manner. The data is imprecise in the sense that information sources often cannot indicate when, how many, and how frequently updates really happened. We tackle the challenge by developing a scalable multiagent model in which each agent performs autonomous mining and cooperative monitoring. It significantly outperforms state-of-the-art IM techniques in capturing a higher percentage of updates in a timelier manner by conducting fewer inquiries.
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.