12394638
Planar Graphs with Circular Chromatic Numbers between 3 and 4
This paper proves that for every rational number r between 3 and 4, there exists a planar graph G whose circular chromatic number is equal to r. Combining this result with a recent result of Moser, we arrive at the conclusion that every rational number r between 2 and 4 is the circular chromatic number of a planar graph.
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).
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.
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.
10777147
Circular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs
This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphsG(Z,D) for various distance setsD. In particular, we determine these numbers for thoseDsets of size two, for some specialDsets of size three, forD= {1, 2,···,m,n} with 1 ?m < n, forD= {q,q+1,···,p} withq
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.
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.
1166908
Distributed rate allocation for multi-stream video transmission over ad hoc networks
When multiple video streams are present in an ad hoc network, they share and compete for the common network resources. A rate allocation algorithm must balance the available resources among the video streams in a fair and efficient manner. In addition, it is desirable to have a distributed solution so that nodes do not need to collect global information of the network and that the computational burden can be shared. We propose a distributed rate allocation algorithm which minimizes the total distortion of all video streams. Based on the subgradient method, the proposed scheme only requires link price updates at each relay node based on local observations and rate adaptations at each source node derived from rate-distortion (RD) models of the video. Simulation results show that the proposed scheme can achieve the same optimal rate allocation as that obtained from exhaustive search.
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.
14278266
Harmonic mixtures: combining mixture models and graph-based methods for inductive and scalable semi-supervised learning
Graph-based methods for semi-supervised learning have recently been shown to be promising for combining labeled and unlabeled data in classification problems. However, inference for graph-based methods often does not scale well to very large data sets, since it requires inversion of a large matrix or solution of a large linear program. Moreover, such approaches are inherently transductive, giving predictions for only those points in the unlabeled set, and not for an arbitrary test point. In this paper a new approach is presented that preserves the strengths of graph-based semi-supervised learning while overcoming the limitations of scalability and non-inductive inference, through a combination of generative mixture models and discriminative regularization using the graph Laplacian. Experimental results show that this approach preserves the accuracy of purely graph-based transductive methods when the data has "manifold structure," and at the same time achieves inductive learning with significantly reduced computational cost.