37605729
Circular chromatic numbers of a class of distance graphs
Suppose m,k,s are positive integers with m>sk. Let D"m","k","s denote the set {1,2,...,m}@?{k,2k,...,sk}. The distance graph G(Z,D"m","k","s) has as vertex set all integers Z and edges connecting i and j whenever |i-j|@?D"m","k","s. This paper determines the circular chromatic number of all the distance graphs G(Z,D"m","k","s).
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).
229019
A Machine Learning Approach to TCP Throughput Prediction
TCP throughput prediction is an important capability for networks where multiple paths exist between data senders and receivers. In this paper, we describe a new lightweight method for TCP throughput prediction. Our predictor uses Support Vector Regression (SVR); prediction is based on both prior file transfer history and measurements of simple path properties. We evaluate our predictor in a laboratory setting where ground truth can be measured with perfect accuracy. We report the performance of our predictor for oracular and practical measurements of path properties over a wide range of traffic conditions and transfer sizes. For bulk transfers in heavy traffic using oracular measurements, TCP throughput is predicted within 10% of the actual value 87% of the time, representing nearly a threefold improvement in accuracy over prior history-based methods. For practical measurements of path properties, predictions can be made within 10% of the actual value nearly 50% of the time, approximately a 60% improvement over history-based methods, and with much lower measurement traffic overhead. We implement our predictor in a tool called PathPerf, test it in the wide area, and show that PathPerf predicts TCP throughput accurately over diverse wide area paths.
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.
3331253
Class Noise vs. Attribute Noise: A Quantitative Study
Real-world data is never perfect and can often suffer from corruptions (noise) that may impact interpretations of the data, models created from the data and decisions made based on the data. Noise can reduce system performance in terms of classification accuracy, time in building a classifier and the size of the classifier. Accordingly, most existing learning algorithms have integrated various approaches to enhance their learning abilities from noisy environments, but the existence of noise can still introduce serious negative impacts. A more reasonable solution might be to employ some preprocessing mechanisms to handle noisy instances before a learner is formed. Unfortunately, rare research has been conducted to systematically explore the impact of noise, especially from the noise handling point of view. This has made various noise processing techniques less significant, specifically when dealing with noise that is introduced in attributes. In this paper, we present a systematic evaluation on the effect of noise in machine learning. Instead of taking any unified theory of noise to evaluate the noise impacts, we differentiate noise into two categories: class noise and attribute noise, and analyze their impacts on the system performance separately. Because class noise has been widely addressed in existing research efforts, we concentrate on attribute noise. We investigate the relationship between attribute noise and classification accuracy, the impact of noise at different attributes, and possible solutions in handling attribute noise. Our conclusions can be used to guide interested readers to enhance data quality by designing various noise handling mechanisms.
17434758
An Empirical Study of the Noise Impact on Cost-Sensitive Learning
In this paper, we perform an empirical study of the impact of noise on cost-sensitive (CS) learning, through observations on how a CS learner reacts to the mislabeled training examples in terms of misclassification cost and classification accuracy. Our empirical results and theoretical analysis indicate that mislabeled training examples can raise serious concerns for cost-sensitive classification, especially when misclassifying some classes becomes extremely expensive. Compared to general inductive learning, the problem of noise handling and data cleansing is more crucial, and should be carefully investigated to ensure the success of CS learning.
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.