15506913
A class of perfect graphs containing P6
Let P6 denote the induced path on six nodes. We prove that if a perfect graph G contains P6 as an induced subgraph but not two families introduced by Conforti and Cornuejols then G is bipartite or disconnected, or G has a star cutset.
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.
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.
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.
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.
292448
Efficient Network Utilization for Multimedia Wireless Networks
In this paper, we present an access scheme to satisfy the QoS requirements for two classes of traffic during the contention phase of packet-switched wireless communications. In the proposed scheme, difierent classes of users contend with other users for resources based on controlled class-dependent permission probabilities. We prove that our algorithm is stable for a large class of arrival processes. Under certain QoS requirements, we derive an upper-bound on the throughput for a general class of random access algorithms. We show that the throughput of our algorithm asymptotically approaches this upper-bound. We also show, through numerical examples, that our algorithm achieves high network utilization.
6185811
An efficient large deformation method using domain decomposition
Efficiently simulating large deformations of flexible objects is a challenging problem in computer graphics. In this paper, we present a physically based approach to this problem, using the linear elasticity model and a finite elements method. To handle large deformations in the linear elasticity model, we exploit the domain decomposition method, based on the observation that each sub-domain undergoes a relatively small local deformation, involving a global rigid transformation. In order to efficiently solve the deformation at each simulation time step, we pre-compute the object responses in terms of displacement accelerations to the forces acting on each node, yielding a force-displacement matrix. However, the force-displacement matrix could be too large to handle for densely tessellated objects. To address this problem, we present two methods. The first method exploits spatial coherence to compress the force-displacement matrix using the clustered principal component analysis method; and the second method pre-computes only the force-displacement vectors for the boundary vertices of the sub-domains and resorts to the Cholesky factorization to solve the acceleration for the internal vertices of the sub-domains. Finally, we present some experimental results to show the large deformation effects and fast performance on complex large scale objects under interactive user manipulations.
10851913
Taming heterogeneity - the Ptolemy approach
Modern embedded computing systems tend to be heterogeneous in the sense of being composed of subsystems with very different characteristics, which communicate and interact in a variety of ways-synchronous or asynchronous, buffered or unbuffered, etc. Obviously, when designing such systems, a modeling language needs to reflect this heterogeneity. Today's modeling environments usually offer a variant of what we call amorphous heterogeneity to address this problem. This paper argues that modeling systems in this manner leads to unexpected and hard-to-analyze interactions between the communication mechanisms and proposes a more structured approach to heterogeneity, called hierarchical heterogeneity, to solve this problem. It proposes a model structure and semantic framework that support this form of heterogeneity, and discusses the issues arising from heterogeneous component interaction and the desire for component reuse. It introduces the notion of domain polymorphism as a way to address these issues.
39184835
Improved Robustness in Time Series Analysis of Gene Expression Data by Polynomial Model Based Clustering
Microarray experiments produce large data sets that often contain noise and considerable missing data. Typical clustering methods such as hierarchical clustering or partitional algorithms can often be adversely affected by such data. This paper introduces a method to overcome such problems associated with noise and missing data by modelling the time series data with polynomials and using these models to cluster the data. Similarity measures for polynomials are given that comply with commonly used standard measures. The polynomial model based clustering is compared with standard clustering methods under different conditions and applied to a real gene expression data set. It shows significantly better results as noise and missing data are increased.