Flexible coloring

Motivated by reliability considerations in data deduplication for storage systems, we introduce the problem of flexible coloring. Given a hypergraph H and the number of allowable colors k, a flexible coloring of H is an assignment of one or more colors to each vertex such that, for each hyperedge, it is possible to choose a color from each vertex?s color list so that this hyperedge is strongly colored (i.e., each vertex has a different color). Different colors for the same vertex can be chosen for different incident hyperedges (hence the term flexible). The goal is to minimize color consumption, namely, the total number of colors assigned, counting multiplicities. Flexible coloring is NP-hard and trivially approximable, where s is the size of the largest hyperedge, and n is the number of vertices. Using a recent result by Bansal and Khot, we show that if k is constant, then it is UGC-hard to approximate to within a factor of s−ε, for arbitrarily small constant ε>0. Lastly, we present an algorithm with an approximation ratio, where k^′ is number of colors used by a strong coloring algorithm for H.     

Consensus models: Computational complexity aspects in modern approaches to the list coloring problem

In the paper we study new approaches to the problem of list coloring of graphs. In the problem we are given a simple graph G=(V,E) and, for every v∈V, a nonempty set of integers S(v); we ask if there is a coloring c of G such that c(v)∈S(v) for every v∈V. Modern approaches, connected with applications, change the question—we now ask if S can be changed, using only some elementary transformations, to ensure that there is such a coloring and, if the answer is yes, what is the minimal number of changes. In the paper for studying the adding, the trading and the exchange models of list coloring, we use the following transformations:

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adding of colors (the adding model): select two vertices u, v and a color c∈S(u); add c to S(v), i.e. set S(v):=S(v)∪{c};

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trading of colors (the trading model): select two vertices u, v and a color c∈S(u); move c from S(u) to S(v), i.e. set S(u):=S(u)?{c} and S(v):=S(v)∪{c};

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exchange of colors (the exchange model): select two vertices u, v and two colors c∈S(u), d∈S(v); exchange c with d, i.e. set S(u):=(S(u)?{c})∪{d} and S(v):=(S(v)?{d})∪{c}.

Our study focuses on computational complexity of the above models and their edge versions. We consider these problems on complete graphs, graphs with bounded cyclicity and partial k-trees, receiving in all cases polynomial algorithms or proofs of NP-hardness.     

锡盐着色膜颜色与氧化膜中Sn含量的关系

对锡盐电解着色膜的颜色深浅与氧化膜中Ｓｎ含量两者之间的关系进行了研究。此外还探讨了锡盐电解着色液中镍离子和亚铁离子在电解着色过程中所起的作用。     

两类完全4-部图的邻点可区别正常边染色

主要讨论了两类完全4-部图的邻点可区别正常边染色.具体验证了邻点可区别正常边染色色数的猜想对该类图是成立的.     

指导cache静态划分的程序性能profiling优化技术

对于共享cache的多核处理器,如何管理好各个核对cache的利用,对于充分发挥多核处理器性能是很关键的问题.目前采用的cache替换方法程序间会出现性能干扰,cache静态划分技术则是通过为同时运行的程序分配不同的空间来解决性能干扰问题.为了给程序分配合适大小的cache空间,需要对程序进行性能profiling,即事先多遍运行收集程序在各种cache容量下的性能数据,这种性能profiling方法开销巨大,影响实用.为了解决性能profiling需要多遍运行程序的问题,提出了只需单遍运行的程序性能profiling优化技术.该技术利用在线的phase分析技术识别程序的运行阶段,避免对相同阶段的重复profiling;同时分析程序各phase的性能同cache容量变化的关系趋势,对于性能不敏感的容量变化则不进行profiling,降低开销.在程序运行结束后通过程序各phase在cache各种容量下的性能来估计程序在各容量下的整体性能,以指导cache静态划分.实验表明,该技术的开销仅为7%,而该方法指导的cache划分比未划分时有8%的性能改进,同多遍运行的程序性能profiling指导的cache划分性能相比仅有1%的下降.     

完全图的点可区别强全染色算法

根据图的点可区别全染色的定义,结合完全图的对称性,提出一种新的点可区别强全染色算法。该算法将需要填充的颜色分为超色数和正常色数2个部分,在得到染色数量和染色次数的前提下,对超色数进行染色以增强算法收敛性。实验结果表明,该算法具有较低的时间复杂度。     

DirectX在有限元分析结果三维彩色云图生成方法中的应用

本文采用扫描线法,将DirectX技术应用到有限元分析结果三维彩色云图的生成方法中,利用DirectX的实体填充模式和高洛德着色模式完成云图渲染绘制。通过实例验证,本文给出的云图生成方法不仅效果好、速度快,而且方法简单、实用。该方法适用于各类场值三维彩色云图的生成,具有很好的通用性和扩展性。     

若干多重Mycielski图的邻点可区别Ⅰ-全色数

根据路和星、圈的多重Mycielski图的结构性质,用穷染递推的方法,讨论了图Mn(Cm)和Mn(Pm),以及Mn(Sm)的邻点可区别I-全染色,得到了图Mn(Sm)和Mn(Pm)的邻点可区别I-全色数等于它们的最大度,图Mn(Cm)的邻点可区别I-全色数在m=4,5时等于它的最大度加1,其余情况等于它的最大度,即分别给出图Mn(Sm)和Mn(Cm)、Mn(Pm)一种染色方案。     

整数距离图G(Dm,3)的点线性荫度

整数距离图G(D)以全体整数为顶点集，顶点u,v相邻当且仅当|u-v|∈D，其中D是一个正整数集.对于m＞3，设Dm,3={1,2,…,m}＼{3}，本文得到了G(Dm,3)的点线性荫度的上界和下界并决定出了它在某些较小的m上的确切值.     

圆染色在交通信号灯相位优化设计中的应用

通过引入图论中“最大独立集”、“圆染色”、“圆色数”的概念,将其运用于城市路口交通信号灯最优相位个数的最优相位设计上,并将交通信号灯最优相位归结为其交通流模型图的圆色数.在这篇文章中,根据实际生活中常见四、五交叉路口的各种交通状况,由车流的冲突关系给出交通流模型图并由圆染色的定义及一些已有的结论证明出这些图的圆色数.