2506645
Maximum genus and maximum nonseparating independent set of a 3-regular graph
Abstract A set J ⊆ V is called a nonseparating independent set (nsis) of a connected graph G = ( V , E ), if J is an independent set of G , i.e., E ∩ { uv | ∀ u , v ∈ J } = 0, and G − J is connected. We call z ( G ) = max J {| J || J is an nsis of G} the nsis number of G . Let G be a 3-regular connected graph; we prove that the maximum genus, denoted by γ M ( G ), of G is equal to z ( G ). Then, according to this result, some new characterizations of the maximum genus γ M ( G ) are obtained.
35771956
Maximum genus of a graph in terms of its embedding properties
Let G be a graph that is cellularly embedded in the projective plane such that the dual graph is Hamiltonian. Then we prove that G is upper embeddable. In the meantime we also obtain the same result for other general orientable surfaces if the dual graph contains a separating Hamilton circuit.
8485722
The maximum genus of graphs with diameter three
Abstract This paper shows that if G is a simple graph with diameter three then G is up-embeddable unless G is either a Δ2-graph (Fig. 1) or a Δ3-graph (Fig. 2) with ξ(G) = 2, i.e., the maximum genus γM(G) = (β(G) − 2)/2.
7153278
Maximum genus and girth of graphs
Abstract In this paper, a lower bound on the maximum genus of a graph in terms of its girth is established as follows: let G be a simple graph with minimum degree at least three, and let g be the girth of G. Then γ(G)⩾ g−2 2(g−1) β(G)+ 1 g−1 except for G=K 4 , where β(G) denotes the cycle rank of G and K4 is the complete graph with four vertices.
39392055
Maximum genus and chromatic number of graphs
Let T be a spanning tree of a connected graph G. Denote by @x(G,T) the number of components in [email protected]?E(T) with odd number of edges. The value min"[email protected](G,T) is known as the Betti deficiency of G, denoted by @x(G), where the minimum is taken over all spanning trees T of G. It is known (N.H. Xuong, J. Combin. Theory 26 (1979) 217-225) that the maximum genus of a graph is mainly determined by its Betti deficiency @x(G). Let G be a k-edge-connected graph (k=<3) whose complementary graph has the chromatic number m. In this paper we prove that the Betti deficiency @x(G) is bounded by a function f"k(m) on m, and the bound is the best possible. Thus by Xuong's maximum genus theorem we obtain some new results on the lower bounds of the maximum genus of graphs.
25290683
Maximum genus, connectivity and minimal degree of graphs
This paper is devoted to the lower bounds on the maximum genus of graphs. A simple statement of our results in this paper can be expressed in the following form: Let G be a k-edge-connected graph with minimum degree @d, for each positive integer k(= =f(@d)@b(G), and furthermore that lim"@d"->"~f(@d)=1/2, where @b(G)=|E(G)|-|V(G)|+1 is the cycle rank of G. The result shows that lower bounds of the maximum genus of graphs with any given connectivity become larger and larger as their minimum degree increases, and complements recent results of several authors.
3154384
Text clustering with extended user feedback
Text clustering is most commonly treated as a fully automated task without user feedback. However, a variety of researchers have explored mixed-initiative clustering methods which allow a user to interact with and advise the clustering algorithm. This mixed-initiative approach is especially attractive for text clustering tasks where the user is trying to organize a corpus of documents into clusters for some particular purpose (e.g., clustering their email into folders that reflect various activities in which they are involved). This paper introduces a new approach to mixed-initiative clustering that handles several natural types of user feedback. We first introduce a new probabilistic generative model for text clustering (the SpeClustering model) and show that it outperforms the commonly used mixture of multinomials clustering model, even when used in fully autonomous mode with no user input. We then describe how to incorporate four distinct types of user feedback into the clustering algorithm, and provide experimental evidence showing substantial improvements in text clustering when this user feedback is incorporated.
16023484
Asymptotically convergent modified recursive least-squares with data-dependent updating and forgetting factor
Continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances. This paper investigates an algorithm which has the capability of eliminating these difficulties. Based on a set theoretic assumption, the algorithm yields modified least-squares estimates with a forgetting factor. It updates the estimates selectively depending on whether the observed data contain sufficient information. The information evaluation required at each step involves very simple computations. In addition, the parameter estimates are shown to converge asymptotically to a region around the true parameter at an exponential rate.
14183146
Replicated condition monitoring
A condition monitoring system tracks real-world variables and alerts users when a predefined condition becomes true, e.g., when stock price drops, or when a nuclear reactor over-heats. Replication of monitoring servers can reduce the probability that an important alert is missed. However, replicated independent servers can sometimes report “conflicting” alerts to the user, causing confusion. In this paper, we study the problem of replicated condition monitoring. We identify and formally define three desirable properties of a replicated system, namely, orderedness, consistency, and completeness. We propose new monitoring algorithms that enforce some or all of the desired properties in different scenarios.
16574049
Feature Selection with Rough Sets for Web Page Classification
Web page classification is the problem of assigning predefined categories to web pages. A challenge in web page classification is how to deal with the high dimensionality of the feature space. We present a feature reduction method based on the rough set theory and investigate the effectiveness of the rough set feature selection method on web page classification. Our experiments indicate that rough set feature selection can improve the predictive performance when the original feature set for representing web pages is large.
10970909
MAPGrid: A New Architecture for Empowering Mobile Data Placement in Grid Environments
The rising popularity of mobile applications and devices has brought about an enhanced interest in infrastructure support for mobile computing. Our work focuses on the development of a mobile grid infrastructure called MAPGrid (mobile applications on Grids), where grid resources are exploited as proxies to enable advanced mobile applications. However, intermittent availability of grid resources presents challenges for data-intensive mobile applications. In this paper, we propose novel methodologies for placing mobile data on grid proxies. We introduce a notion of two-tier architecture for MAPGrid, where the upper tier captures grid related features and the lower tier represents features associated with mobile environments. We further develop an intelligent mobile data placement mechanism that effectively balances tradeoffs between replication cost and data access cost by leveraging knowledge of grid availability and mobile data request patterns. Through extensive experimentation, we illustrate the superiority of the proposed techniques over several popular data placement strategies.