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.     

异构网络资源分配：改进多对一转移匹配

随着无线业务的急剧增长,短缺的频谱资源正面临着巨大挑战。采用无线异构网络被视作解决此问题,提高频谱利用率的一种有效手段。但是,由于宏蜂窝和微蜂窝共享相同频谱资源,同层和跨层干扰非常严重,这时如何合理进行资源分配成了一个棘手的问题。针对该问题,根据匹配理论提出了一种改进多对一转移匹配算法进行资源分配。该算法在满足交换条件下,通过微蜂窝用户不断地交换其匹配资源,最终形成稳定转移匹配。仿真结果表明,所提改进转移匹配算法较传统转移匹配算法和改进Gale-Shapley匹配算法性能更易收敛到最优解,同时提高了频谱利用率,降低了计算复杂度。     

基于TLA+的AFDX冗余管理算法的改进

为了在航空应用中得到更加安全可靠的通讯系统,就目前普遍应用的标准以太网可能会出现的问题,提出了用行为时序逻辑TLA对AFDX冗余管理算法进行形式化分析.在适当的环境中,根据安全性、活性、可用性3个性质,得到两个冗余管理的推论,根据这些性质和推论,提出了3个冗余管理算法,并用TLA+语言进行详细的描述.通过模型检测,表明出RMA13为最优算法.     

运动估值的实用快速算法

现有的许多有关运动估值的快速算法,都存在着匹配速度快与匹配精度差的矛盾。文章在分析已有典型快速算法优缺点的基础上,提出了解决这一矛盾的分步逼近的新算法——“迂回逼近法”;算法选择了快捷和更为准确的搜索路径,且对程序的实现技术作了有效改进,其最终匹配结果具有全匹配算法的精度和典型快速算法的速度。文中说明了算法原理,程序技术和对比实验结果。     

基于稳定匹配的容器部署策略的优化

Docker的发展使得操作系统级虚拟化的容器渐渐兴起,容器即服务(CaaS)也越来越普及。随着容器技术的发展,容器将成为云环境中的主要部署模型,但针对容器的整合部署技术还未得到广泛的研究。容器化云环境中的容器数量众多,如何将众多的容器部署到合适的虚拟机以降低 数据中心能耗,成为了一个亟待解决的问题。因此,文中创新性地将机器学习中的几种相似度计算方法作为稳定匹配算法的偏好规则,同时将已经拟分配过容器的虚拟机继续加入偏好列表,从而将一对一的稳定婚姻匹配算法改进为多对一的稳定匹配,解决了将容器整合到虚拟机上的初始化部署问题。仿真实验结果表明 , 采用优化的稳定匹配算法来初始化将部署容器时,不仅SLA违规较低,而且比FirstFit,MostFull以及Random算法分别约节能12.8%,34.6%和30.87%,其中使用欧氏距离作为稳定匹配算法偏好规则的节能效果最好。     

基于SURF和快速近似最近邻搜索的图像匹配算法

针对高维特征向量存在的最近邻匹配正确率低的问题, 提出了一种基于SURF和快速近似最近邻搜索的图像匹配算法。首先用Fast-Hessian 检测子进行特征点检测, 并生成SURF特征描述向量; 然后通过快速近似最近邻搜索算法得到初匹配点对, 再对得出的单向匹配结果进行双向匹配; 最后采用鲁棒性较好的PROSAC算法进一步剔除误匹配点对。实验证明了该算法不仅提高了SURF算法匹配的正确率, 还保证了算法的实时性。     

基于多邻域支持技术的迭代式角点匹配算法

角点匹配是立体视觉研究中的一个重要问题,文中针对该问题提出一种基于多邻域支持技术的迭代式角点匹配算法.该算法首先使用Marr和Frisby提出的立体匹配的五大约束限定搜索区域,然后使用了多邻域支持技术对点特征相似性的评价方法进行了改进,最后引入了左/右以及上/下两种对称性测试过程和迭代技术以提高匹配的精度.这些技术解决了传统匹配算法实时性差、精确度低的问题.仿真实验表明,该算法是一种快速、稳定并且实用的角点匹配算法.     

基于视频的大空间建筑消防系统研究

针对基于视频的大空间建筑火灾消防存在的实时性和有效性问题,提出了一种基于改进的自适应差分进化算法的摄像机自标定方法。用基于比值法与相关函数法融合的SURF火灾图像特征点匹配算法,快速得到准确的匹配点对;进行摄像机自标定,用较为准确的匹配点对求得基本矩阵F,利用绝对二次曲线的性质,得到优化函数。利用基于改进的差分进化算法对其进行优化,求得摄像机内参数,得到火源的三维信息。实验结果证明,该方法短时间内,算出了较为准确的火源的空间三维信息,实时性和精确度均能够满足火灾消防的标准,有效地进行灭火。     

一种快速的加权矢量图像匹配方法

为了解决工业生产中产品的快速定位,提出了一种快速的图像匹配方法。首先运用Surf算法提取出图像的特征点,然后运用形状上下文特征进行匹配,得到图像的大致位置,最后依据特征点描述子及其位置特征,通过加权矢量匹配的方式得到图像的精确位置,实现产品的快速定位。该算法稳定性高,计算速度快。实验结果表明,该算法能满足实时的工业生产要求。     

混合共享认知无线网络信道分配算法

混合频谱共享是适应认知用户不同地理分布的有效频谱共享模式。信道分配是无线通信网络中关键的问题之一,近年来得到了广泛研究。集中式信道分配算法是最常用的算法形式,但在认知无线电网络这种分布式系统中,集中式算法不易实现。将混合共享认知无线网络的信道分配问题构建为一对一的匹配博弈,提出了分布式用户-信道匹配算法。该算法数学复杂度低,且能够达到稳定匹配。仿真结果表明,算法收敛时间短,稳定匹配状态下的平均传输速率与使用匈牙利算法的最优分配算法所获得传输速率相接近,远优于随机分配算法的传输速率。     

Manipulation complexity and gender neutrality in stable marriage procedures

The stable marriage problem is a well-known problem of matching men to women so that no man and woman who are not married to each other both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors, to hospitals to matching students to schools. A well-known algorithm to solve this problem is the Gale–Shapley algorithm, which runs in quadratic time in the number of men/women. It has been proven that stable marriage procedures can always be manipulated. Whilst the Gale–Shapley algorithm is computationally easy to manipulate, we prove that there exist stable marriage procedures which are NP-hard to manipulate. We also consider the relationship between voting theory and stable marriage procedures, showing that voting rules which are NP-hard to manipulate can be used to define stable marriage procedures which are themselves NP-hard to manipulate. Finally, we consider the issue that stable marriage procedures like Gale–Shapley favour one gender over the other, and we show how to use voting rules to make any stable marriage procedure gender neutral.     

Stable Marriage with General Preferences

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable marriage where preferences are allowed to have ties and to be incomplete. As a result, we prove that deciding the existence of a stable matching in our model is NP-complete. Complementing this negative result we present a polynomial-time algorithm for the above decision problem in a significant class of instances where the preferences are asymmetric. We also present a linear programming formulation whose feasibility fully characterizes the existence of stable matchings in this special case. Finally, we use our model to study a long standing open problem regarding the existence of cyclic 3D stable matchings. In particular, we prove that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP-complete, showing this way that a natural attempt to resolve the existence (or not) of 3D stable matchings is bound to fail.     

A Polynomial-Time Algorithm to Find von Neumann-Morgenstern Stable Matchings in Marriage Games

This paper considers von Neumann-Morgenstern (vNM) stable sets in marriage games. Ehlers (Journal of Economic Theory 134: 537–547, 2007) showed that if a vNM stable set exists in a marriage game, the set is a maximal distributive lattice of matchings that includes all core matchings. To determine what matchings form a vNM stable set, we propose a polynomial-time algorithm that finds a man-optimal matching and a woman-optimal matching in a vNM stable set of a given marriage game. This algorithm also generates a modified preference profile such that a vNM stable set is obtained as the core of a marriage game with the modified preference profile. It is well known that cores of marriage games are nonempty. However, the nonemptiness of cores does not imply the existence of a vNM stable set. It is proved using our algorithm that there exists a unique vNM stable set for any marriage game.     

A unified approach to finding good stable matchings in the hospitals/residents setting

The hospitals/residents (HR) problem is a many-to-one generalization of the stable marriage (SM) problem. Researchers have been interested in variants of stable matchings that either satisfy a set of additional contraints or are optimal with respect to some cost function. In this paper, we show that broad classes of feasibility and optimization stable matching problems in the HR setting can be solved efficiently provided certain tasks (such as checking the feasibility of a stable matching or computing the cost of a stable matching) can also be done efficiently. To prove our results, we make use of an HR instance’s meta-rotation poset to explore its stable matchings. An algorithm that can discover all the meta-rotations of the instance serves as a starting point for all our algorithms.     

面向移动边缘计算网络的高能效计算卸载算法

移动边缘计算（mobile edge computing,MEC）是一种高效的技术,通过将计算密集型任务从移动设备卸载到边缘服务器,使终端用户实现高带宽、低时延的目标.移动边缘计算环境下的计算卸载在减轻用户负载和增强终端计算能力等方面发挥着重要作用.考虑了服务缓存,提出一种云-边-端协同的计算卸载框架,在该框架中引入D2D （device-to-device,D2D）通信和机会网络.基于建立的模型,将计算卸载决策问题转化为一个混合整数非线性规划问题,并对无线特性和移动用户之间的非合作博弈交互制定了一个迭代机制来共同确定计算卸载方案.对提出的计算卸载算法从理论上证明了多用户计算卸载博弈模型为严格势力场博弈（exact potential game,EPG）,卸载决策可获得全网范围内的最优效益.考虑到服务器的计算资源、卸载任务数据量和任务延迟需求,提出对用户和MEC服务器之间最佳用户关联匹配算法.最后,模拟结果表明,卸载决策算法具有较快的收敛速度,并在能效方面优于其他基准算法.     

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds.     

聚集组播组-树匹配算法

组播的状态伸缩性问题是目前困扰组播技术发展的一个难题。该文分析了一种解决组播状态问题的方法——聚集组播和聚集组播的组-树匹配算法。提出一种动态匹配算法——FDMA,通过对网络中聚集树的管理来减少匹配次数,从而提高聚集速度。在仿真实验中,FDMA算法使组-树匹配次数减少了80%以上,聚集组播的实时性得到了较大的提高。     

一种基于马尔科夫网的本体匹配算法

概率模型是解决不确定性推理和数据分析的有效工具。针对本体匹配的不确定性,提出一种基于马尔科夫网的本体匹配改进算法。采用多种传统匹配算法计算相似度矩阵,改进相似度传播规则,添加2种结构稳定性约束规则和1种Disjoint一致性约束规则,定义其对应团的势函数。根据相似度矩阵和上述规则,给出马尔科夫网的构造方法,使用循环置信度传播算法计算随机变量的后验概率,依据后验概率得到最后的本体匹配结果。在OAEI2010数据集上进行实验,结果表明,与iMatch本体匹配系统相比,该算法能有效降低概率模型的复杂度,提高本体匹配的准确率和召回率。