A new polynomial-time algorithm for the maximum weighted (χ(G) — 1)-coloring problem in comparability graphs

For a weighted graph G = (V, E), the maximum weightedk-coloring problem is to color a set of vertices of maximum weight usingk colors. In this paper we are interested in solving this problem in comparability graphs. For these graphs, as shown by Cameron, the problem can be translated into a dual transportation problem. Let (G) denote the chromatic number of a comparability graphG. We prove that whenk is equal to (G) — 1, the problem can be solved more efficiently by finding a maximum weighted stable set in a bipartite graph. Maximum matching algorithms can be used in the unweighted case.This work was supported by an NSERC International Fellowship to the University of Montréal, and by NSERC #OGP0105384.     

STAR-CCM+使用技巧(续1)

1 如何通过Sim模板缩短从导入模型到执行计算过程的工作时间? 对于几何模型不同但边界条件、计算条件甚至网格尺寸范围相同的算例,STAR-CCM+可将已计算过的sim文件作为新模型的计算模板,大大节省流程中网格尺寸调试、边界条件和计算条件等设定所花费的工时.     

A Parallel Implementation Model of HPARLOG

In this paper,a new parallel logic programming language——HPARLOG developed by usis described,and a new scheme for the AND-parallelism implementation in logic programminglanguage is proposed.This scheme not only resolves the instantiation conflict on sharing-variables,thoroughly explores the parallelism of the programs with incrementally constructeddata structure,but also decreases the dynamic complexity of the programs.In addition,apscudo-copy based memory management scheme to enhance the locality of goal processes andlower the overhead of program execution is proposed.     

STAR CCM+使用技巧(续1)

对于几何模型不同但边界条件、计算条件甚至网格尺寸范围相同的算例,STAR—CCM＋可将已计算过的sim文件作为新模型的计算模板,大大节省流程中网格尺寸调试、边界条件和计算条件等设定所花费的工时．     

环Fp+uFp+vFp上的(1+u+v)-循环码

常循环码是一类重要的线性码,由于其纠错性能易于分析,因而广泛应用于实践中,同时,利用有限环上常循环码还可以直接构造最优线性码。定义了有限非链环[Fp+uFp+vFp]上[(1+u+v)]-循环码的相关概念,讨论了其生成多项式;引入了一种新的Gray映射[?],证明了该环上[(1+u+v)]-循环码在此Gray映射[?]下的[p]元象是一个长为[2pn]的2-准循环码,并由此构造出了两个最优二元准循环码。     

Parallel Transitional Rules of Items in Parsing

Context-free Grammars（CFGs）, which are connected with linear Arrays, can be parsed in parallel on IL（i） structures and store items of the form [ij,B→η＊] in these structures. In this algorithm, what can be found in this transferring process are the efficiency and superiority of the algorithm. The transferring rules of IL（i） are portrayed in detail in this paper, and it can avoid the uselessness of transferring items in these circular structures, and the transferring process under these definitions is also given out.     

On Parallel Evaluation of Ordered Attribute Grammars

In this paper,a parallel algorithm is presented for the evaluation of orgered attribute grammars.The parallelism is achieved by constructing the so-called paralled visit sequences and accordingly augmenting the ordinary evaluation driver as well.For experimental purposes,the algorithm has been implemented by simulation.     

Parallel Execution of Prolog on Shared-Memory Multiprocessors

Logic programs offer many opportunities for the exploitation of parallelism.But the parallel execution of a task incurs various overheads.This paper focuses on the issues relevant to parallelizing Prolog on shared-memory multiprocessors efficiently.     

Log-Linear Convergence and Divergence of the Scale-Invariant (1+1)-ES in Noisy Environments

Noise is present in many real-world continuous optimization problems. Stochastic search algorithms such as Evolution Strategies (ESs) have been proposed as effective search methods in such contexts. In this paper, we provide a mathematical analysis of the convergence of a (1+1)-ES on unimodal spherical objective functions in the presence of noise. We prove for a multiplicative noise model that for a positive expected value of the noisy objective function, convergence or divergence happens depending on the infimum of the support of the noise. Moreover, we investigate convergence rates and show that log-linear convergence is preserved in presence of noise. This result is a strong theoretical foundation of the robustness of ESs with respect to noise.     

A note on “Regular bipolar fuzzy graphs” Neural Computing and Applications 21(1) (2012) 197–205

In this note, we show by examples that Definitions 3.3, 3.5, Propositions 3.9, 3.10 and Theorem 3.17 in the paper by Akram and Dudek (Neural Comput Appl 21(1):197–205, 2012) contain some flaws, and then, we presented the updated results. Hence, we introduce generalized regular bipolar fuzzy graphs.

     

On equitable colouring of Knödel graphs

The notion of equitable colouring was introduced by Meyer in 1973. In this paper we find the equitable chromatic number χ₌ for the line graph of Knödel graphs L(W_{Δ, n}), central graph of Knödel graphs C(W_{Δ, n}) and corona graph of Knödel graphs W_{Δ, m}° W_{Δ, n}. As a by-product we obtain a new class of graphs that confirm Equitable Colouring Conjecture.     

On an infinite family of graphs with information ratio 2 − 1/k

In this paper we consider the secret sharing problem on special access structures with minimal qualified subsets of size two, i.e. secret sharing on graphs. This means that the participants are the vertices of the graph and the qualified subsets are the subsets of V(G) spanning at least one edge. The information ratio of a graph G is denoted by R(G) and is defined as the ratio of the greatest size of the shares a vertex has to remember and of the size of the secret. Since the determination of the exact information ratio is a non-trivial problem even for small graphs (i.e. for V(G) = 6), every construction can be of particular interest. Let k be the maximal degree in G. In this paper we prove that R(G) = 2 ? 1/k for every graph G with the following properties: (A) every vertex has at most one neighbour of degree one; (B) vertices of degree at least 3 are not connected by an edge; (C) the girth of the graph is at least 6. We prove this by using polyhedral combinatorics arguments and the entropy method.     

Implementation of GAMMA on a Massively Parallel Computer

The GAMMA paradigm is recently proposed by Banatre and Metayer to describe the systematic construction of parallel programs without introducing artificial sequentiality.This paper presents two synchronous execution models for GAMMA and discusses how to implement them on MasPar MP-1,a massively data parallel computer.The results show that GAMMA paradign can be implemented very naturally on data parallel machines,and very high level language,such as GAMMA in which parallelism is left implicit,is suitable for specifying massively parallel applications.     

(2+1)维Bogoyavlenskii-Schiff方程的精确解

应用简单方程法求得(2+1)维Bogoyavlenskii-Schiff方程的精确解,这种方法对于研究非线性发展方程具有非常广泛的应用意义.     

On the complexity of variations of mixed domination on graphs†

This paper is motivated by the concept of the mixed domination problem on graphs and dedicated to the complexity of variations of the problem such as the signed mixed domination, signed edge domination, minus mixed domination, and minus edge domination problems. In this paper, we present NP-completeness and MAX SNP-hardness results for some of them, and present a general framework of solving these problems and various dominating and covering problems for trees in linear time.     

Vertex fault tolerance of optimal-κ graphs and super-κ graphs

A connected graph G is optimal-κ if κ(G)=δ(G). It is super-κ if every minimum vertex cut isolates a vertex. An optimal-κ graph G is m-optimal-κ if for any vertex set S⊆V(G) with |S|?m, G−S is still optimal-κ. We define the vertex fault tolerance with respect to optimal-κ, denoted by Oκ(G), as the maximum integer m such that G is m-optimal-κ. The concept of vertex fault tolerance with respect to super-κ, denoted by Sκ(G), is defined in a similar way. In this paper, we show that min{κ₁(G)−δ(G),δ(G)−1}?Oκ(G)?δ(G)−1 and min{κ₁(G)−δ(G)−1,δ(G)−1}?Sκ(G)?δ(G)−1, where κ₁(G) is the 1-extra connectivity of G. Furthermore, when the graph is triangle free, more refined lower bound can be derived for Oκ(G).