217118
The circular chromatic number of series-parallel graphs of large odd girth
Suppose G is a series-parallel graph. We prove that if G has odd girth at least 6k - 1 then χc(G) ≤ 8k/(4k - 1); if G has odd girth at least 6k + 1 then χc(G) ≤ (4k + 1)/2k; if G has odd girth at least 6k + 3 then χc(G) ≤ (4k + 3)/(2k + 1).
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.
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.
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.
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).
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.
16957901
Bridging Local and Global Data Cleansing: Identifying Class Noise in Large, Distributed Data Datasets
To cleanse mislabeled examples from a training dataset for efficient and effective induction, most existing approaches adopt a major set oriented scheme: the training dataset is separated into two parts (a major set and a minor set). The classifiers learned from the major set are used to identify noise in the minor set. The obvious drawbacks of such a scheme are twofold: (1) when the underlying data volume keeps growing, it would be either physically impossible or time consuming to load the major set into the memory for inductive learning; and (2) for multiple or distributed datasets, it can be either technically infeasible or factitiously forbidden to download data from other sites (for security or privacy reasons). Therefore, these approaches have severe limitations in conducting effective global data cleansing from large, distributed datasets.In this paper, we propose a solution to bridge the local and global analysis for noise cleansing. More specifically, the proposed effort tries to identify and eliminate mislabeled data items from large or distributed datasets through local analysis and global incorporation. For this purpose, we make use of distributed datasets or partition a large dataset into subsets, each of which is regarded as a local subset and is small enough to be processed by an induction algorithm at one time to construct a local model for noise identification. 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 data 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 and eliminate the noisy examples. Experimental results and comparative studies on both real-world and synthetic datasets are reported to evaluate the effectiveness and efficiency of the proposed approach.
1251013
Congestion-aware rate allocation for multipath video streaming over ad hoc wireless networks
For multipath video streaming over ad hoc wireless networks, received video quality is influenced by both the encoder performance and the delayed packet arrivals due to limited bandwidth. We propose a rate allocation scheme to optimize the expected received video quality based on simple models of encoder rate-distortion performance and network rate-congestion tradeoffs. Given the embedded bit-streams of a group of video frames and the cross traffic condition on a given set of paths, a gradient descent method is used to determine the amount of bits to be transmitted over the multiple paths for each frame. Two rate allocation strategies, layered representation and partial repetition are also investigated. Simulation results of video streaming over a 15-node wireless ad hoc network demonstrates the benefit of performing rate allocation optimization over a simple heuristic scheme. It is also shown that while layered representation is more efficient for mild delay constraints, partial repetition is more robust against packet losses.
5621999
Accelerated Kernel Feature Analysis
A fast algorithm, Accelerated Kernel Feature Analysis (AKFA), that discovers salient features evidenced in a sample of n unclassified patterns, is presented. Like earlier kernel-based feature selection algorithms, AKFA implicitly embeds each pattern into a Hilbert space, H, induced by a Mercer kernel. An \ell-dimensional linear subspace of H is iteratively constructed by maximizing a variance condition for the nonlinearly transformed sample. This linear subspace can then be used to define more efficient data representations and pattern classifiers. AKFA requires O(\elln2) operations, as compared to 0(n^3) for Sch¨olkof, Smola, and M¨uller’s Kernel Principal Component Analysis (KPCA), and O(\ell^2 n^2) for Smola, Mangasarian, and Sch¨olkopf’s Sparse Kernel Feature Analysis (SKFA). Numerical experiments show that AKFA can generate more concise feature representations than both KPCA and SKFA, and demonstrate that AKFA obtains similar classification performance as KPCA for a face recognition problem.
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.