一种求解二部图最大匹配问题新算法及其应用

提出了解决二部图最大匹配问题的分层网络优化算法,并应用新算法对排课问题进行求解。定义了分层网络的概念及匹配的规则,结合广度优先搜索策略生成分层网络体系,然后按网络逆序找出最大匹配。实验表明,算法在解决大规模二部图最大匹配的理论问题和实际应用问题时均能获得准确的结果,具备良好的性能。     

基于Edmonds-Karp算法的输入排队调度

输入排队Crossbar调度算法是以获得交换机的输入端口和输出端口最大匹配,从而得到高吞吐量为目的.因而在调度算法理论研究中把应用了二部图最大匹配的Maximum Size Matching和 Maximum Weight Matching算法作为目前各种调度算法性能评价标准.Edmonds-Karp算法是图论中求解网络最大流的经典算法之一.该文介绍了如何使用Edmonds-Karp算法求解二部图的最大匹配问题,并且应用算法于输入排队调度算法仿真中,得出经典MSM和MWM算法的性能仿真曲线,为进一步研究调度算法打下了理论基础.     

二部图最大匹配问题的分层网络优化模型

为解决二部图最大匹配问题,提出了分层网络及网络逆序的概念,在此基础上建立了一种分层网络优化模型及其算法。给出了算法的思想、步骤、实例、时间复杂度分析,概述了求解二部图最大匹配问题的常见算法,与分层网络优化算法进行比较。实验验证,算法可读性强,易于理解和操作,在解决大规模二部图最大匹配问题时具有良好的性能。     

二部图的所有极大匹配

二部图作为一种非常重要的数据结构有很多特殊性质,针对文献[4]中的二部图的所有极大匹配求解算法,给出了反例证明了该算法是错误的,同时证明了二部图的所有极大匹配的求解是NP难问题.     

使用Ford-Fulkerson算法研究输入排队调度

Ford-Fulkerson算法是图论中求解网络最大流的经典算法之一。输入排队Crossbar调度算法是以获得交换机的输入端口和输出端口最大匹配,从而得到高吞吐量。因而在调度算法理论研究中把应用了二部图最大匹配的MaximumSizeMatching(MSM)和MaximumWeightMatching(MWM)算法作为目前各种调度算法性能评价标准。论文介绍了如何使用Ford-Fulkerson算法求解二部图的最大匹配,并且应用算法于输入排队调度算法仿真中,得出对应典型算法MSM和MWM的性能仿真曲线,从而为进一步研究调度算法打下理论基础。     

计算机视觉中图匹配研究进展: 从二图匹配迈向多图匹配

图匹配试图求解二图或多图之间节点的对应关系.在图像图形领域,图匹配是一个历久弥新的基础性问题.从优化的角度来看,图匹配问题是一个组合优化问题,且在一般情形下具有非确定性多项式复杂程度(non-deter-ministic polynomial, NP)难度的性质.在过去数十年间,出现了大量求解二图匹配的近似算法,并在各个领域得到了较为广泛的应用.然而,受限于优化问题本身的理论困难和实际应用中数据质量的种种限制,各二图匹配算法在匹配精度上的性能日益趋近饱和.相比之下,由于引入了更多信息且往往更符合实际问题的设定,多图的协同匹配则逐渐成为了一个新兴且重要的研究方向.本文首先介绍了经典的二图匹配方法,随后着重介绍近年来多图匹配方法的最新进展和相关工作.最后,本文讨论了图匹配未来的发展.     

二部图所有极大匹配的求解算法

二部图是一种十分重要的数据结构。在对二部图及匹配的概念进行了阐述后。给出了求二部图所有极大匹配的算法。该算法也可用于求二部图的所有最大匹配和完全匹配。用C语言程序验证了此算法的有效性。     

稳定婚姻匹配问题的一个快速枚举算法

稳定匹配问题是算法理论中的典型问题之一,稳定婚姻匹配问题则是一种解决二部图匹配问题的模型。论文对稳定婚姻匹配问题进行了简单的阐述,并介绍了求解典型稳定婚姻问题的Gale-Shapley算法的基本思想及其性质。为了快速求出所有的稳定匹配结果,提出了基于先序遍历森林的快速枚举算法。由Gale-Shapley算法的性质得到一个定理及其推论,利用得到的推论对算法做了进一步改进和优化。在满足推论的特定条件下,提高了算法的执行效率。     

平衡图匹配方法在多视角图像配准中的研究

在多视角图像处理中,多点匹配是一个基本的问题。针对有较多制约因素的多点匹配问题,对现有的光谱匹配技术进行两点改进:首先提出一种新的光谱松弛技术用以求解匹配函数的近似解,其次将现有的相容性矩阵重构为二分图边矩阵并进行双随机归一化,减小噪声对结果的影响。在基于CAVIAR与PETS2009数据集上的实验证明,所提出的算法可以很好地完成图匹配,并且有较高的精度与较好的鲁棒性。     

稳定完备婚姻问题的算法及推广

稳定匹配问题是算法理论中的典型问题之一,稳定婚姻匹配问题则是一种解决二部图匹配问题的模型.论文对稳定婚姻匹配问题进行了简单的阐述,并介绍了求解典型稳定婚姻问题的Gale-Shapley算法的基本思想及其性质,并且再推广到广义的延迟认可算法,解决现实生活中的公司招聘员工等的案例.     

On maximum induced matchings in bipartite graphs

The problem of finding a maximum induced matching is known to be NP-hard in general bipartite graphs. We strengthen this result by reducing the problem to some special classes of bipartite graphs such as bipartite graphs with maximum degree 3 or C₄-free bipartite graphs. On the other hand, we describe a new polynomially solvable case for the problem in bipartite graphs which deals with a generalization of bi-complement reducible graphs.     

Hardness and approximation of minimum maximal matchings

In this paper, we consider the minimum maximal matching problem in some classes of graphs such as regular graphs. We show that the minimum maximal matching problem is NP-hard even in regular bipartite graphs, and a polynomial time exact algorithm is given for almost complete regular bipartite graphs. From the approximation point of view, it is well known that any maximal matching guarantees the approximation ratio of 2 but surprisingly very few improvements have been obtained. In this paper we give improved approximation ratios for several classes of graphs. For example any algorithm is shown to guarantee an approximation ratio of (2-o(1)) in graphs with high average degree. We also propose an algorithm guaranteeing for any graph of maximum degree Δ an approximation ratio of (2?1/Δ), which slightly improves the best known results. In addition, we analyse a natural linear-time greedy algorithm guaranteeing a ratio of (2?23/18k) in k-regular graphs admitting a perfect matching.     

An adjustable linear time parallel algorithm for maximum weight bipartite matching

We present a parallel algorithm for finding a maximum weight matching in general bipartite graphs with an adjustable time complexity of using O(nmax(2ω,4+ω)) processing elements for ω?1. Parameter ω is not bounded. This is the fastest known strongly polynomial parallel algorithm to solve this problem. This is also the first adjustable parallel algorithm for the maximum weight bipartite matching problem in which the execution time can be reduced by an unbounded factor. We also present a general approach for finding efficient parallel algorithms for the maximum matching problem.     

Finding Maximum Induced Matchings in Subclasses of Claw-Free and <Emphasis Type="Italic">P</Emphasis><Subscript>5</Subscript>-Free Graphs,and in Graphs with Matching and Induced Matching of Equal Maximum Size

In a graph G a matching is a set of edges in which no two edges have a common endpoint. An induced matching is a matching in which no two edges are linked by an edge of G. The maximum induced matching (abbreviated MIM) problem is to find the maximum size of an induced matching for a given graph G. This problem is known to be NP-hard even on bipartite graphs or on planar graphs. We present a polynomial time algorithm which given a graph G either finds a maximum induced matching in G, or claims that the size of a maximum induced matching in G is strictly less than the size of a maximum matching in G. We show that the MIM problem is NP-hard on line-graphs, claw-free graphs, chair-free graphs, Hamiltonian graphs and r-regular graphs for r \geq 5. On the other hand, we present polynomial time algorithms for the MIM problem on (P ₅,D _m )-free graphs, on (bull, chair)-free graphs and on line-graphs of Hamiltonian graphs.     

基于稳定匹配的电子中介匹配研究

介绍了稳定性双边匹配的概念,概括了Gale-Sharply和H-R算法求解1-1和1-k的计算过程.考虑商品的多属性,给出了交易者按综合满意程度对满足自己约束对方的排序计算方法.将Gale-Sharply和H-R算法从理论上扩展到"p-k"情况,用来解决电子中介处理稳定的多对多双边匹配问题.最后证明了扩展算法所得结果的稳定性,并给出了算例.     

Matching Algorithms Are Fast in Sparse Random Graphs

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every non-maximum matching has an augmenting path of length O(log n). This implies that augmenting path algorithms like the Hopcroft-Karp algorithm for bipartite graphs and the Micali-Vazirani algorithm for general graphs, which have a worst case running time of O(m√n), run in time O(m log n) with high probability, where m is the number of edges in the graph. Motwani proved these results for random graphs when the average degree is at least ln (n) [Average Case Analysis of Algorithms for Matchings and Related Problems, Journal of the ACM, 41(6):1329-1356, 1994]. Our results hold if only the average degree is a large enough constant. At the same time we simplify the analysis of Motwani.     

基于赋权二部图的记录簇匹配模型及其算法

通过一组成员记录表示实体时,相似记录匹配问题被扩展为记录簇匹配问题。提出2种记录簇匹配模式,应用赋权二部图理论建立记录簇匹配数学模型,设计记录簇上下界匹配算法。快速推导出记录簇匹配阈值的上下界,以减少记录簇子记录最大权的匹配次数。实验结果证明该算法能提高记录簇匹配精度和计算效率。     

面向子流的低延迟数据调度算法

P2P流媒体是分发流媒体数据的高效方式,而数据传输延迟是决定P2P流媒体系统性能的重要参数。在分析"拉"模式数据调度模式传输延迟的基础上,本文在"推"、"拉"混合的调度模式下提出一种新的面向子流的低延迟数据调度算法。首先子流的调度问题被转换成等价的带权二部图匹配问题,其次针对转换后的二部图改进匈牙利算法,提出最小延迟、最大匹配的启发式匹配算法。该算法在保证最大匹配的同时使得每条子流的延迟尽可能地低。模拟实验表明本文的算法能够极大降低数据传输延迟。     

一种可重构阵列的最小瑕点覆盖算法

关于可重构阵列的瑕点覆盖问题受到了很多文献的关注，特别地，关于可重构阵列的最小瑕点覆盖问题等价于二分图的受约束最小点覆盖问题，并被证明是NP-完全问题。针对本问题提出的算法运行时间为O(1．19^k kn)，这里k为可替换行与列的数目，改进了原有的最好结果，其运行时间为0(1．266k kn)，较好地组合并扩展了研究参数计算的最新技术与经典匹配理论，且具有较好的实用价值。这是关于可重构阵列的最小瑕点覆盖问题算法又一较大的改进，也是目前最小点覆盖问题相关参数算法的较有意义的改进。     

Constant factor approximation algorithms for the densest k-subgraph problem on proper interval graphs and bipartite permutation graphs

The densest k-subgraph problem asks for a k-vertex subgraph with the maximum number of edges. This problem is NP-hard on bipartite graphs, chordal graphs, and planar graphs. A 3-approximation algorithm is known for chordal graphs. We present -approximation algorithms for proper interval graphs and bipartite permutation graphs. The latter result relies on a new characterisation of bipartite permutation graphs which may be of independent interest.