15307840
Fractional chromatic number and circular chromatic number for distance graphs with large clique size
Let Z be the set of all integers and M a set of positive integers. The distance graph G(Z,M) generated by M is the graph with vertex set Z and in which i and j are adjacent whenever |i − j| ∈ M . Supported in part by the National Science Foundation under grant DMS 9805945. Supported in part by the National Science Council, R. O. C., under grant NSC892115-M-110-012.
206792834
Star chromatic numbers of graphs
We investigate the relation between the star-chromatic number χ(G) and the chromatic number χ(G) of a graphG. First we give a sufficient condition for graphs under which their starchromatic numbers are equal to their ordinary chromatic numbers. As a corollary we show that for any two positive integersk, g, there exists ak-chromatic graph of girth at leastg whose star-chromatic number is alsok. The special case of this corollary withg=4 answers a question of Abbott and Zhou. We also present an infinite family of triangle-free planar graphs whose star-chromatic number equals their chromatic number. We then study the star-chromatic number of An infinite family of graphs is constructed to show that for each ε>0 and eachm≥2 there is anm-connected (m+1)-critical graph with star chromatic number at mostm+ε. This answers another question asked by Abbott and Zhou.
42953989
The game coloring number of pseudo partial k-trees
Abstract This paper introduces a new class of graphs: (a,b)-pseudo partial k-trees. In some sense, the parameters (a,b) measure a graph's deviation from being a partial k-tree. In particular, a (0,0)-pseudo partial k-tree is just a partial k-tree. We discuss the game coloring number (as well as the game chromatic number) of (a,b)-pseudo partial k-trees, and prove that the game coloring number of an (a,b)-pseudo partial k-tree is at most 3k+2a+b+2. In particular, the game coloring number of a partial k-tree is at most 3k+2. This reduces considerably the previous known upper bound for the game chromatic number of a partial k-tree. Then we describe another strategy for Alice for playing the game, which gives a better upper bound for the game coloring number of (a,b)-pseudo partial 2-trees. Namely, we prove that the game coloring number of an (a,b)-pseudo partial 2-tree is at most a+b+8. By using this result, we prove that the game coloring number of a graph embeddable on an orientable surface of genus g⩾1 is at most ⌊ 1 2 (3 1+48g +23)⌋. This is the first upper bound for the game coloring number of such graphs, and it also improves considerably the previous known upper bound for the game chromatic number of such graphs. Moreover, the strategy for Alice introduced in this paper for playing the game can be considered as a common generalization of the previous known strategies for playing the game on forests, interval graphs, outerplanar graphs and planar graphs.
7791840
Pseudo-Hamiltonian-connected graphs
Abstract Given a graph G and a positive integer k , denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k . A graph G is called pseudo- k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo- k Hamiltonian-connected for some positive integer k . This paper proves that a graph G is pseudo-Hamiltonian-connected if and only if for every non-empty proper subset X of V(G) , |N(X)|>|X| . The proof of the characterization also provides a polynomial-time algorithm that decides whether or not a given graph is pseudo-Hamiltonian-connected. The characterization of pseudo-Hamiltonian-connected graphs also answers a question of Richard Nowakowski, which motivated this paper.
17776907
Circular perfect graphs
For 1 ≤ d ≤ k, let Kk/d be the graph with vertices 0, 1, · · · , k − 1, in which i ∼ j if d ≤ |i − j| ≤ k − d. The circular chromatic number χc(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to Kk/d. The circular clique number ωc(G) of G is the maximum of those k/d for which Kk/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G we have χc(H) = ωc(H). This paper surveys results on circular perfect graphs.
5956515
Homomorphisms to oriented paths
Abstract Given an oriented path P , we characterize those digraphs G which are homomorphic to P . The characterization equates the nonexistence of a homomorphism G → P with the existence of a homomorphism W → G , for some oriented path W which is not homomorphic to P . This result complements the recent polynomial time algorithm of Welzl et al. to find such a homomorphism (if one exists).
34769702
JavaAHP: a web-based decision analysis tool for natural resource and environmental management
Natural resource and environmental management invariably involves multiple issues, multiple criteria and multiple stakeholders. A large amount of social, economic and environmental information needs to be linked to government policies, stakeholder values, public opinions and management goals. A systematic approach to decision analysis involved in natural resource and environmental management is required to improve the quality of the decision and justify the actions to be taken. The Analytical Hierarchy Process (AHP) provides a methodology for multi-criteria analysis and decision making. It allows critical examination of the underlying assumptions, consistency of the judgements, and facilitates the incorporation of qualitative and subjective considerations into quantitative factors for decision making. JavaAHP is a software tool, which implements the AHP. It uses the AHP methodology to model an environmental problem, evaluate relative desirability of alternatives, and organise the information and judgements used in decision making. JavaAHP is deployed on the World Wide Web (WWW) and can be accessed globally. It takes advantages of the WWW with wide availability, Web resource integration and cross-platform capabilities. This paper introduces the major features of JavaAHP and its potential applications in natural resource and environmental management.
2283419
Nonparametric Transforms of Graph Kernels for Semi-Supervised Learning
We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.
11534248
Mining in Anticipation for Concept Change: Proactive-Reactive Prediction in Data Streams
Prediction in streaming data is an important activity in the modern society. Two major challenges posed by data streams are (1) the data may grow without limit so that it is difficult to retain a long history of raw data; and (2) the underlying concept of the data may change over time. The novelties of this paper are in four folds. First, it uses a measure of conceptual equivalence to organize the data history into a history of concepts. This contrasts to the common practice that only keeps recent raw data. The concept history is compact while still retains essential information for learning. Second, it learns concept-transition patterns from the concept history and anticipates what the concept will be in the case of a concept change. It then proactively prepares a prediction model for the future change. This contrasts to the conventional methodology that passively waits until the change happens. Third, it incorporates proactive and reactive predictions. If the anticipation turns out to be correct, a proper prediction model can be launched instantly upon the concept change. If not, it promptly resorts to a reactive mode: adapting a prediction model to the new data. Finally, an efficient and effective system RePro is proposed to implement these new ideas. It carries out prediction at two levels, a general level of predicting each oncoming concept and a specific level of predicting each instance's class. Experiments are conducted to compare RePro with representative existing prediction methods on various benchmark data sets that represent diversified scenarios of concept change. Empirical evidence offers inspiring insights and demonstrates the proposed methodology is an advisable solution to prediction in data streams.
9200586
Scalable Inductive Learning on Partitioned Data
With the rapid advancement of information technology, scalability has become a necessity for learning algorithms to deal with large, real-world data repositories. In this paper, scalability is accomplished through a data reduction technique, which partitions a large data set into subsets, applies a learning algorithm on each subset sequentially or concurrently, and then integrates the learned results. Five strategies to achieve scalability (Rule-Example Conversion, Rule Weighting, Iteration, Good Rule Selection, and Data Dependent Rule Selection) are identified and seven corresponding scalable schemes are designed and developed. A substantial number of experiments have been performed to evaluate these schemes. Experimental results demonstrate that through data reduction some of our schemes can effectively generate accurate classifiers from weak classifiers generated from data subsets. Furthermore, our schemes require significantly less training time than that of generating a global classifier.
2122679
Combining proactive and reactive predictions for data streams
Mining data streams is important in both science and commerce. Two major challenges are (1) the data may grow without limit so that it is difficult to retain a long history; and (2) the underlying concept of the data may change over time. Different from common practice that keeps recent raw data, this paper uses a measure of conceptual equivalence to organize the data history into a history of concepts. Along the journey of concept change, it identifies new concepts as well as re-appearing ones, and learns transition patterns among concepts to help prediction. Different from conventional methodology that passively waits until the concept changes, this paper incorporates proactive and reactive predictions. In a proactive mode, it anticipates what the new concept will be if a future concept change takes place, and prepares prediction strategies in advance. If the anticipation turns out to be correct, a proper prediction model can be launched instantly upon the concept change. If not, it promptly resorts to a reactive mode: adapting a prediction model to the new data. A system RePro is proposed to implement these new ideas. Experiments compare the system with representative existing prediction methods on various benchmark data sets that represent diversified scenarios of concept change. Empirical evidence demonstrates that the proposed methodology is an effective and efficient solution to prediction for data streams.