28132040
Circular Colouring and Orientation of Graphs
This paper proves that if a graph G has an orientation D such that for each cycle C with d|C| (mod k) ∈ {1,2 ..... 2d- 1} we have |C|/|C+|≤k/d and |c|/|c-|≤k/d,then G has a (k,d)-colouring and hence χc(G) ≤ k/d. This is a generalization of a result of Tuza (J. Combin. Theory Ser. B 55 (1992), 236-243) concerning the vertex colouring of a graph, and is also a strengthening of a result of Goddyn et al. (J. Graph Theory 28 (1998), 155-161) concerning the relation between orientation and circular chromatic number of a graph.
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.
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.
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).
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.
31029747
Design Tools for Application Specific Embedded Processors
A variety of factors make it increasingly difficult and expensive to design and manufacture traditional Application Specific Integrated Circuits (ASICs). Consequently, programmable alternatives are more attractive than ever. The flexibility provided by programmability comes with a performance and power overhead. This can be significantly mitigated by using application specific platforms, also referred to as Application Specific Embedded Processors, or Application Specific Instruction Set Processors (ASIPs).ASIPs and the embedded software applications running on them, require specialized design tools - both during architectural evaluation to provide feedback on the suitability of the architecture for the application; as well as during system implementation to ensure efficient mapping and validation of design constraints. These functions result in requirements different from those of traditional software development environments. The first requirement is retargetability, especially during the early architectural evaluation stage where a rapid examination of design alternatives is essential. The second requirement is for additional metrics such as power consumption, real-time constraints and code size.This paper describes a set of design tools and associated methodology designed to meet the challenges posed by architectural evaluation and software synthesis. This work is part of the MESCAL (Modern Embedded Systems, Compilers, Architectures, and Languages) project.
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.
9200586
Scalable Inductive Learning on Partitioned Data
With the rapid advancement of information technology, scalability has become a necessity for learning algorithms to deal with large, real-world data repositories. In this paper, scalability is accomplished through a data reduction technique, which partitions a large data set into subsets, applies a learning algorithm on each subset sequentially or concurrently, and then integrates the learned results. Five strategies to achieve scalability (Rule-Example Conversion, Rule Weighting, Iteration, Good Rule Selection, and Data Dependent Rule Selection) are identified and seven corresponding scalable schemes are designed and developed. A substantial number of experiments have been performed to evaluate these schemes. Experimental results demonstrate that through data reduction some of our schemes can effectively generate accurate classifiers from weak classifiers generated from data subsets. Furthermore, our schemes require significantly less training time than that of generating a global classifier.
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.