8130739
Homomorphisms to oriented cycles
We discuss the existence of homomorphisms to oriented cycles and give, for a special class of cyclesC, a characterization of those digraphs that admit, a homomorphism toC. Our result can be used to prove the multiplicativity of a certain class of oriented cycles, (and thus complete the characterization of multiplicative oriented cycles), as well as to prove the membership of the corresponding decision problem in the classNPϒcoNP. We also mention a conjecture on the existence of homomorphisms to arbitrary oriented cycles.
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.
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.
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
1654569
Qualitative Camera Motion Classification for Content-Based Video Indexing
Due to the fact that the camera motion usually imply some hints which are helpful in bridging the gap between computationally available features and semantic interpretations, extensive researches have been executed to extract them for various purposes. However, these strategies fail to classify the camera rotation; furthermore, their performance might be significantly reduced by considerable noise or error in extracted features. In this paper, a robust camera motion classification strategy is proposed. We use the mutual relationship between motion vectors for motion classification. Given any two motion vectors in each P-frame, four types of mutual relationships between them are classified, then, a 14-bins feature vector is constructed to characterize the statistical motion information for the P-frame. Finally, the qualitative classification is executed by considering all achieved statistical information.
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.
31441115
Seeded Semantic Object Generation toward Content-Based Video Indexing
A novel semantic object generation algorithm is proposed by collaborative integration of a new feature-based image segmentation technique and a seeded region aggregation procedure. The homogeneous image regions with closed boundaries are obtained by integrating the results of color edge detection and seeded region growing procedures. The object seeds are then distinguished from these homogeneous image regions. The semantic objects are finally generated by a seeded region aggregation procedure. The extracted semantic objects can then be tracked along the time axis. The video objects can then be used as the basic units for content-based video indexing.
10041607
Comparison of Modularization Methods in Application to Different Biological Networks
Most biological networks have been proposed to possess modular organization, which increases the robustness, flexibility, and stability of networks. Many clustering methods have been used in mining biological data and partitioning complex networks into functional modules. Most of these methods require presetting the number of modules and therefore can potentially obtain biased results. The Markov clustering method (MCL) and the simulated annealing module-detection method (SA) eliminate this requirement and can objectively separate relatively dense subgraphs. In this paper, we compared these two module-detection methods for three types of biological data: protein family classification, microarray clustering, and modularity of metabolic networks. We found that these two methods show differential advantages for different biological networks. In the case of the gene network based on Affymetrix microarray spike data, MCL exactly identified the same number of groups and same contents in each group set by the spike data. In the case of the gene network derived from actual expression data, although neither of the two methods can perfectly recover the natural classification, MCL performs slightly better than SA. However, with increased random noise added to the gene expression values, SA generates better modular structures with higher modularity. Next we compared the modularization results of MCL and SA for protein family classification and found the modules detected by SA could not be well matched with the Structural Classification of Proteins (SCOP database), which suggests that MCL is ideally suited to the rapid and accurate detection of protein families. In addition, we used both methods to detect modules in the metabolic network of E. coli. MCL gives a trivial clustering, which generates biologically insignificant modules. In contrast, SA detects modules well corresponding to the KEGG functional classification. Moreover the modularity for several other metabolic networks detected by SA is also much higher than that by MCL. In summary, MCL is more suited to modularize relatively complete and definite data, such as a protein family network. In contrast, SA is less sensitive to noise such as experimental error or incomplete data and outperforms MCL when modularizing gene networks based on microarray data and large scale metabolic networks constructed from incomplete databases.
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.