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.
1319456
Multiplicativity of acyclic local tournaments
A homomorphism of a digraph to another digraph is an edge-preserving vertex mapping. A digraphH is said to be multiplicative if the set of digraphs which do not admit a homomorphism toH is closed under categorical product. In this paper we discuss the multiplicativity of acyclic Hamiltonian digraphs, i.e., acyclic digraphs which contains a Hamiltonian path. As a consequence, we give a complete characterization of acyclic local tournaments with respect to multiplicativity.
5666902
The chromatic numbers of distance graphs
Abstract Suppose D is a subset of all positive integers L . The distance graph G ( L , D ) is the graph with vertex set L and two vertices x , y are adjacent if | x − y | ∈ D . This paper studies the chromatic number of G ( L , D ). We shall concentrate on the case that | D | = 3 and give a complete classification of those D = { a , b , c } for which b is a multiple of a and χ ( G ( L , D )) = 3.
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.
41218825
Relaxed game chromatic number of graphs
This paper discusses a coloring game on graphs. Let k, d be non-negative integers and C a set of k colors. Two persons, Alice and Bob, alternately color the vertices of G with colors from C, with Alice having the first move. A color i is legal for an uncolored vertex x if by coloring x with color i, the subgraph of G induced by those vertices of color i has maximum degree at most d. Each move of Alice or Bob colors an uncolored vertex with a legal color. The game is over if either all vertices are colored, or no more vertices can be colored with a legal color. Alice's goal is to produce a legal coloring which colors all the vertices of G, and Bob's goal is to prevent this from happening. We shall prove that if G is a forest, then for k = 3, d ≥ 1, Alice has a winning strategy. If G is an outerplanar graph, then for k = 6 and d ≥ 1, Alice has a winning strategy.
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.
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.
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.
1057136
Corrective Classification: Classifier Ensembling with Corrective and Diverse Base Learners
Empirical studies on supervised learning have shown that ensembling methods lead to a model superior to the one built from a single learner under many circumstances especially when learning from imperfect, such as biased or noise infected, information sources. In this paper, we provide a novel corrective classification (C2) design, which incorporates error detection, data cleansing and Bootstrap sampling to construct base learners that constitute the classifier ensemble. The essential goal is to reduce noise impacts and eventually enhance the learners built from noise corrupted data. We further analyze the importance of both the accuracy and diversity of base learners in ensembling, in order to shed some light on the mechanism under which C2 works. Experimental comparisons will demonstrate that C2 is not only superior to the learner built from the original noisy sources, but also more reliable than bagging or the aggressive classifier ensemble (ACE), which are two degenerate components/variants of C2.
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.
18367158
A distributed database server for continuous media
In our project, we are adopting a new approach for handling video data. We view the video as a well-defined data type with its own description, parameters and applicable methods. The system is based on PREDATOR, an open-source object-relational DBMS. PREDATOR uses Shore as the underlying storage manager. Supporting video operations (storing, searching-by-content and streaming) and new query types (query-by-example and multi-feature similarity searching) requires major changes in many of the traditional system components. More specifically, the storage and buffer manager has to deal with huge volumes of data with real-time constraints. Query processing has to consider the video methods and operators in generating, optimizing and executing the query plans.