12655450
The circular chromatic index of graphs of high girth
We show that for each @e>0 and each integer @D>=1, there exists a number g such that for any graph G of maximum degree @D and girth at least g, the circular chromatic index of G is at most @[email protected]
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.
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.
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.
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).
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
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.
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.
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.
31920818
Automatic model-based semantic object extraction algorithm
Automatic image segmentation and object extraction play an important role in supporting content-based image coding, indexing, and retrieval. However, the low-level visual homogeneity critical (like color, texture, intensity, and so on) for segmentation do not lead to semantic objects directly because a semantic object can contain totally different gray levels, color, or texture. We propose an automatic model-based semantic object extraction algorithm by integrating object seeds with their region constraint graphs (perceptual models). Images are first partitioned into a set of homogeneous regions with accurate boundaries by integrating the results obtained by similarity-based region growing and edge detection procedures. We propose a 1-D fast entropic thresholding technique for determining the thresholds used in region growing and edge detection automatically. The object seeds, which are the intuitive and representative parts of semantic objects, are then distinguished from these homogeneous image regions. A seeded region aggregation procedure is used for merging the adjacent regions of a detected object seed to give a semantic object according to the perceptual model of the object. We focus on semantic human object generation by taking faces as object seeds and using a ratio-based perceptual model.
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.