Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

低能电子衍射表面结构分析中引入全局优化算法——遗传算法的研究

将遗传算法(GAs)应用到低能电子衍射(LEED)表面结构分析方法中,编制了Gas-LEED结构自动搜寻的计算程序,并以Pt(111)-p(2×2)O吸附系统为例,获得了具有全局优化特点的结构参数。     

An approximation algorithm for the generalized assignment problem

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep _ij and incurs a cost ofc _ij ; each machinei is available forT _i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T _i time units.We also extend this result to a variant of the problem where, instead of a fixed processing timep _ij , there is a range of possible processing times for each machine—job pair, and the cost linearly increases as the processing time decreases. We show that these results imply a polynomial-time 2-approximation algorithm to minimize a weighted sum of the cost and the makespan, i.e., the maximum job completion time. We also consider the objective of minimizing the mean job completion time. We show that there is a polynomial-time algorithm that, given valuesM andT, either proves that no schedule of mean job completion timeM and makespanT exists, or else finds a schedule of mean job completion time at mostM and makespan at most 2T. Research partially supported by an NSF PYI award CCR-89-96272 with matching support from UPS, and Sun Microsystems, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.Research supported in part by a Packard Fellowship, a Sloan Fellowship, an NSF PYI award, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.     

生物医学检测中太赫兹光谱技术的算法研究

基于太赫兹波的非电离、非侵入性、高穿透性、高分辨率和光谱指纹特征,太赫兹光谱技术在生物医学领域具有巨大潜力.基于太赫兹光谱技术和不同的分析算法,不同研究小组实现了对混合物样品的定性、定量识别.然而,实际的生物混合物样品中通常包含水在内的不同成分,进而导致光谱的信噪比较差,导致最终的光谱分析结果误差较大.对于此类问题,降...     

遗传算法在构象搜寻中的应用

遗传算法是一种模仿自然进化进程的新颖的启发式优化方法。通过它，人们可以在计算机上对所需的各种问题实施进化操作，最终产生理想的结果。遗传算法现已被广泛于计算机辅助设计、工程设计、系统模拟等领域并取得了极大的成功。本文拟对遗传算法在对大、中、小分子的构象搜寻中的应用作一较全面的综述。     

Solving multiobjective,multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

In this paper, we solve instances of the multiobjective multiconstraint (or multidimensional) knapsack problem (MOMCKP) from the literature, with three objective functions and three constraints. We use exact as well as approximate algorithms. The exact algorithm is a properly modified version of the multicriteria branch and bound (MCBB) algorithm, which is further customized by suitable heuristics. Three branching heuristics and a more general purpose composite branching and construction heuristic are devised. Comparison is made to the published results from another exact algorithm, the adaptive ε-constraint method [Laumanns, M., Thiele, L., Zitzler, E., 2006. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169, 932–942], using the same data sets. Furthermore, the same problems are solved using standard multiobjective evolutionary algorithms (MOEA), namely, the SPEA2 and the NSGAII. The results from the exact case show that the branching heuristics greatly improve the performance of the MCBB algorithm, which becomes faster than the adaptive ε -constraint. Regarding the performance of the MOEA algorithms in the specific problems, SPEA2 outperforms NSGAII in the degree of approximation of the Pareto front, as measured by the coverage metric (especially for the largest instance).     

Randomized broadcast in networks

In this paper we study the rate at which a rumor spreads through an undirected graph. This study has two important applications in distributed computation: in simple, robust and efficient broadcast protocols, and in the maintenance of replicated databases.     

Rivality index neighbourhood algorithm with density and distances weighted schemes for the building of robust QSAR classification models with high reliable applicability domain

The rivality index (RI) is a normalized distance measurement between a molecule and their first nearest neighbours providing a robust prediction of the activity of a molecule based on the known activity of their nearest neighbours. Negative values of the RI describe molecules that would be correctly classified by a statistic algorithm and, vice versa, positive values of this index describe those molecules detected as outliers by the classification algorithms. In this paper, we have described a classification algorithm based on the RI and we have proposed four weighted schemes (kernels) for its calculation based on the measuring of different characteristics of the neighbourhood of molecules for each molecule of the dataset at established values of the threshold of neighbours. The results obtained have demonstrated that the proposed classification algorithm, based on the RI, generates more reliable and robust classification models than many of the more used and well-known machine learning algorithms. These results have been validated and corroborated by using 20 balanced and unbalanced benchmark datasets of different sizes and modelability. The classification models generated provide valuable information about the molecules of the dataset, the applicability domain of the models and the reliability of the predictions.     

Learning Markov chains in fractal compression of image data

In a recent paper [17] we proposed a stochastic algorithm which generates optimal probabilities for the decompression of an image represented by the fixed point of an IFS system (SAOP). We show here that such an algorithm is in fact a non trivial example of Generalized Random System with Complete Connections. We also exhibit a generalization which could represent the solution to the inverse problem for an image with grey levels, if a fixed set of contraction maps is available. Received: 1 July 2002