206571000
The Game Coloring Number of Planar Graphs
This paper discusses a variation of the game chromatic number of a graph: the game coloring number. This parameter provides an upper bound for the game chromatic number of a graph. We show that the game coloring number of a planar graph is at most 19. This implies that the game chromatic number of a planar graph is at most 19, which improves the previous known upper bound for the game chromatic number of planar 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).
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.
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.
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.
6174679
Correlation Clustering for Crosslingual Link Detection
The crosslingual link detection problem calls for identifying news articles in multiple languages that report on the same news event. This paper presents a novel approach based on constrained clustering. We discuss a general way for constrained clustering using a recent, graph-based clustering framework called correlation clustering. We introduce a correlation clustering implementation that features linear program chunking to allow processing larger datasets. We show how to apply the correlation clustering algorithm to the crosslingual link detection problem and present experimental results that show correlation clustering improves upon the hierarchical clustering approaches commonly used in link detection, and, hierarchical clustering approaches that take constraints into account.
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.
16957901
Bridging Local and Global Data Cleansing: Identifying Class Noise in Large, Distributed Data Datasets
To cleanse mislabeled examples from a training dataset for efficient and effective induction, most existing approaches adopt a major set oriented scheme: the training dataset is separated into two parts (a major set and a minor set). The classifiers learned from the major set are used to identify noise in the minor set. The obvious drawbacks of such a scheme are twofold: (1) when the underlying data volume keeps growing, it would be either physically impossible or time consuming to load the major set into the memory for inductive learning; and (2) for multiple or distributed datasets, it can be either technically infeasible or factitiously forbidden to download data from other sites (for security or privacy reasons). Therefore, these approaches have severe limitations in conducting effective global data cleansing from large, distributed datasets.In this paper, we propose a solution to bridge the local and global analysis for noise cleansing. More specifically, the proposed effort tries to identify and eliminate mislabeled data items from large or distributed datasets through local analysis and global incorporation. For this purpose, we make use of distributed datasets or partition a large dataset into subsets, each of which is regarded as a local subset and is small enough to be processed by an induction algorithm at one time to construct a local model for noise identification. 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 data 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 and eliminate the noisy examples. Experimental results and comparative studies on both real-world and synthetic datasets are reported to evaluate the effectiveness and efficiency of the proposed approach.
9568730
Exploring video content structure for hierarchical summarization
Abstract.In this paper, we propose a hierarchical video summarization strategy that explores video content structure to provide the users with a scalable, multilevel video summary. First, video-shot- segmentation and keyframe-extraction algorithms are applied to parse video sequences into physical shots and discrete keyframes. Next, an affinity (self-correlation) matrix is constructed to merge visually similar shots into clusters (supergroups). Since video shots with high similarities do not necessarily imply that they belong to the same story unit, temporal information is adopted by merging temporally adjacent shots (within a specified distance) from the supergroup into each video group. A video-scene-detection algorithm is thus proposed to merge temporally or spatially correlated video groups into scenario units. This is followed by a scene-clustering algorithm that eliminates visual redundancy among the units. A hierarchical video content structure with increasing granularity is constructed from the clustered scenes, video scenes, and video groups to keyframes. Finally, we introduce a hierarchical video summarization scheme by executing various approaches at different levels of the video content hierarchy to statically or dynamically construct the video summary. Extensive experiments based on real-world videos have been performed to validate the effectiveness of the proposed approach.