32861103
Multiplicativity of Oriented Cycles
We complete the characterization of those oriented cycles C which have the property that the class of digraphs not homomorphic to C is closed under taking the (categorical) product. This is related to Hedetniemi?s conjecture on the chromatic number of the product of undirected graphs. Our main tool is a result concerning the existence of homomorphisms between oriented paths which preserve the initial and terminal vertices. This tool is used to prove that for those cycles C we are interested in, any two oriented paths not homomorphic to C have a common preimage also not homomorphic to C. This "common preimage theorem" implies the multiplicativity of our cycles.
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.
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.
7395446
Segmenting hands of arbitrary color
Hand segmentation is a prerequisite for many gesture recognition tasks. Color has been widely used for hand segmentation. However, many approaches rely on predefined skin color models. It is very difficult to predefine a color model in a mobile application where the light condition may change dramatically over time. We propose a novel statistical approach to hand segmentation based on Bayes decision theory. The proposed method requires no predefined skin color model. Instead it generates a hand color model and a background color model for a given image, and uses these models to classify each pixel in the image as either a hand pixel or a background pixel. Models are generated using a Gaussian mixture model with the restricted EM algorithm. Our method is capable of segmenting hands of arbitrary color in a complex scene. It performs well even when there is a significant overlap between hand and background colors, or when the user wears gloves. We show that the Bayes decision method is superior to a commonly used method by comparing their upper bound performance. Experimental results demonstrate the feasibility of the proposed method.
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.
147992
A hierarchical access control model for video database systems
Content-based video database access control is becoming very important, but it depends on the progresses of the following related research issues: (a) efficient video analysis for supporting semantic visual concept representation; (b) effective video database indexing structure; (c) the development of suitable video database models; and (d) the development of access control models tailored to the characteristics of video data. In this paper, we propose a novel approach to support multilevel access control in video databases. Our access control technique combines a video database indexing mechanism with a hierarchical organization of visual concepts (i.e., video database indexing units), so that different classes of users can access different video elements or even the same video element with different quality levels according to their permissions. These video elements, which, in our access control mechanism, are used for specifying the authorization objects, can be a semantic cluster, a subcluster, a video scene, a video shot, a video frame, or even a salient object (i.e., region of interest). In the paper, we first introduce our techniques for obtaining these multilevel video access units. We also propose a hierarchical video database indexing technique to support our multilevel video access control mechanism. Then, we present an innovative access control model which is able to support flexible multilevel access control to video elements. Moreover, the application of our multilevel video database modeling, representation, and indexing for MPEG-7 is discussed.
6927660
Scalable Representative Instance Selection and Ranking
Finding a small set of representative instances for large datasets can bring various benefits to data mining practitioners so they can (1) build a learner superior to the one constructed from the whole massive data; and (2) avoid working on the whole original dataset all the time. We propose in this paper a scalable representative instance selection and ranking (SRISTAR pronounced 3STAR) mechanism, which carries two unique features: (1) it provides a representative instance ranking list, so that users can always select instances from the top to the bottom, based on the number of examples they prefer; and (2) it investigates the behaviors of the underlying examples for instance selection, and the selection procedure tries to optimize the expected future error. Given a dataset, we first cluster instances into small data cells, each of which consists of instances with similar behaviors. Then we progressively evaluate data cells and their combinations, and order them into a list such that the learners built from the top cells are more accurate
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.