11848222
Asymptotic Clique Covering Ratios of Distance Graphs
Given a finite set D of positive integers, the distance graph G(Z, D) has Z as the vertex set and { ij: | i?j | ?D } as the edge set. Given D, the asymptotic clique covering ratio is defined as S(D) =lim supn?∞ncl(n), where cl(n) is the minimum number of cliques covering any consecutive n vertices of G(Z, D). The parameter S(D) is closely related to the ratio spT(G)?(G)of a graph G, where ?(G) and spT(G) denote, respectively, the chromatic number and the optimal span of a T -coloring of G. We prove that for any finite set D, S(D) is a rational number and can be realized by a `periodical? clique covering of G(Z, D). Then we investigate the problem for which sets D the equality S(D) =?(G(Z, D)) holds. (In general, S(D) ??(G(Z, D)), where ?(G) is the clique number of G.) This problem turns out to be related to T -colorings and to fractional chromatic number and circular chromatic number of distance graphs. Through such connections, we shall show that the equality S(D) =?(G(Z, D)) holds for many classes of distance graphs. Moreover, we raise questions regarding other such connections.
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).
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.
52810083
A hierarchical modeling framework for on-chip communication architectures
The communication sub-system of complex IC systems is increasingly critical for achieving system performance. Given this, it is important that the on-chip communication architecture should be included in any quantitative evaluation of system design during design space exploration. While there are several mature methodologies for the modeling and evaluation of architectures of processing elements, there is relatively little work done in modeling of an extensive range of on-chip communication architectures, and integrating this into a single modeling and simulation environment combining processing element and on-chip communication architectures. This paper describes a modeling framework with accompanying simulation tools that attempts to fill this gap. Based on an analysis of a wide range of on-chip communication architectures, we describe how a specific hierarchical class library can be used to develop new on-chip communication architectures, or variants of existing ones with relatively little incremental effort. We demonstrate this through three case studies including two commercial on-chip bus systems and an on-chip packet switching network. Here we show that through careful analysis and construction it is possible for the modeling environment to support the common features of these architectures as part of the library and permit instantiation of the individual architectures as variants of the library design. As part of this methodology we also show how different levels of abstraction of the model can be supported and viewed as different variants that can be used in an accuracy versus simulation time trade-off.
1052837
Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions
An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning problem is then formulated in terms of a Gaussian random field on this graph, where the mean of the field is characterized in terms of harmonic functions, and is efficiently obtained using matrix methods or belief propagation. The resulting learning algorithms have intimate connections with random walks, electric networks, and spectral graph theory. We discuss methods to incorporate class priors and the predictions of classifiers obtained by supervised learning. We also propose a method of parameter learning by entropy minimization, and show the algorithm's ability to perform feature selection. Promising experimental results are presented for synthetic data, digit classification, and text classification tasks.
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.
205872736
Flatness tolerance evaluation: an approximate minimum zone solution
Abstract This paper is concerned with the problem of flatness tolerance evaluation. First, we introduce the concepts of width and inner radius of point sets, and establish the equivalence between the width of a point set and the inner radius of the convex hull of the self-difference of the set. On this basis, we present an algorithm for calculating the exact minimum zone tolerance of flatness. Second, we prove that an approximation of the inner radius of a convex set can be obtained from the inner radius of the set in fixed direction. On this basis, we present an algorithm for calculating the ‘almost exact’ minimum zone solution. This algorithm is implemented by solving a single linear programming problem, of which the computational complexity is O ( n ). Numerical examples are given to validate the proposed algorithms.
5944615
Eliminating Class Noise in Large Datasets
This paper presents a new approach for identifying and eliminating mislabeled instances in large or distributed datasets. We first partition a dataset into subsets, each of which is small enough to be processed by an induction algorithm at one time. We construct good rules from each subset, and use the good rules to evaluate the whole dataset. For a given instance Ik, two error count variables are used to count the number of times it has been identified as noise by all subsets. The instance with higher error values will have a higher probability of being a mislabeled example. Two threshold schemes, majority and non-objection, are used to identify the noise. Experimental results and comparative studies from real-world datasets are reported to evaluate the effectiveness and efficiency of the proposed approach.