16757439
Odd Hole Recognition in Graphs of Bounded Clique Size
In a graph $G$, an odd hole is an induced odd cycle of length at least 5. A clique of $G$ is a set of pairwise adjacent vertices. In this paper we consider the class ${\cal C}_k$ of graphs whose cliques have a size bounded by a constant $k$. Given a graph $G$ in ${\cal C}_k$, we show how to recognize in polynomial time whether $G$ contains an odd hole.
74880
Line digraphs and coreflexive vertex sets
Abstract The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and n th-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection digraph from a given digraph.
13088953
A polynomial algorithm for recognizing perfect graphs
We present a polynomial algorithm for recognizing whether a graph is perfect, thus settling a long standing open question. The algorithm uses a decomposition theorem of Conforti, Cornuejols and Vuskovic. Another polynomial algorithm for recognizing perfect graphs, which does not use decomposition, was obtained simultaneously by Chudnovsky and Seymour. Both algorithms need a first phase developed jointly by Chudnovsky, Cornuejols, Liu, Seymour and Vuskovic.
2229369
Recognizing Berge Graphs
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(|V (G)|9). This is independent of the recent proof of the strong perfect graph conjecture.
10306588
Word Graphs: The Second Set
In continuation of the paper of Hoede and Li on word graphs for a set of prepositions, word graphs are given for adjectives, adverbs and Chinese classifier words. It is argued that these three classes of words belong to a general class of words that may be called adwords. These words express the fact that certain graphs may be brought into connection with graphs that describe the important classes of nouns and verbs. Some subclasses of adwords are discussed as well as some subclasses of Chinese classifier words.
204983610
Pyramidic Clustering of Large-Scale Microarray Images
With ongoing research and development of imaging techniques such as those involved in brain MRIs, cDNA microarrays and satellite reconnaissance, the need for tools that can intelligently parse larger images is ever increasing. One group of such techniques often used is that of segmentation, an example of which is that of clustering algorithms. In order to deal with large data sets, current approaches require the data to be sampled or summarized before true analysis can take place. In this paper we propose a novel image analysis technique using pyramidic type grouping, namely copasetic clustering, which focuses on the problem of applying traditional clustering techniques to these large-scale image data sets with limited resources. A further benefit of the technique is the transparency of its intermediate clustering steps; when applied to spatial data sets this allows the capture and incorporation of contextual information to improve result accuracy. The algorithm achieves an ∼1--3 dB w-to-noise ratio when compared with the conventional techniques described.
14510898
Evolutionary learning of dynamic probabilistic models with large time lags
In this paper, we explore the automatic explanation of multivariate time series (MTS) through learning dynamic Bayesian networks (DBNs). We have developed an evolutionary algorithm which exploits certain characteristics of MTS in order to generate good networks as quickly as possible. We compare this algorithm to other standard learning algorithms that have traditionally been used for static Bayesian networks but are adapted for DBNs in this paper. These are extensively tested on both synthetic and real-world MTS for various aspects of efficiency and accuracy. By proposing a simple representation scheme, an efficient learning methodology, and several useful heuristics, we have found that the proposed method is more efficient for learning DBNs from MTS with large time lags, especially in time-demanding situations. © 2001 John Wiley & Sons, Inc.
23519212
Lower bounds of length of longest cycles in graphs involving neighborhood unions
Let G be a simple graph of order n. Let NC = min {|N(x)∪N(y)|: xy ∉ E(G)}. Denote by c(G), the circumference of G, the length of a longest cycle in G. In this paper we settle a conjecture of Faudree, Gould, Jacobson and Schelp [4], proving that (a) if G is 3-connected, then c(G) ⩾ min {n, 3(NC + 1)/2}; and (b) if G is 4-connected, then c(G) ⩾ min {n, 2NC}. Two examples are given to show that both bounds are sharp.
368408
A framework for opportunistic scheduling in wireless networks
Abstract We present a method, called opportunistic scheduling, for exploiting the time-varying nature of the radio environment to increase the overall performance of the system under certain quality of service/fairness requirements of users. We first introduce a general framework for opportunistic scheduling, and then identify three general categories of scheduling problems under this framework. We provide optimal solutions for each of these scheduling problems. All the proposed scheduling policies are implementable online; we provide parameter estimation algorithms and implementation procedures for them. We also show how previous work by us and others directly fits into or is related to this framework. We demonstrate via simulation that opportunistic scheduling schemes result in significant performance improvement compared with non-opportunistic alternatives.