Models of Greedy Algorithms for Graph Problems

Borodin et al. (Algorithmica 37(4):295–326, 2003) gave a model of greedy-like algorithms for scheduling problems and Angelopoulos and Borodin (Algorithmica 40(4):271–291, 2004) extended their work to facility location and set cover problems. We generalize their model to include other optimization problems, and apply the generalized framework to graph problems. Our goal is to define an abstract model that captures the intrinsic power and limitations of greedy algorithms for various graph optimization problems, as Borodin et al. (Algorithmica 37(4):295–326, 2003) did for scheduling. We prove bounds on the approximation ratio achievable by such algorithms for basic graph problems such as shortest path, weighted vertex cover, Steiner tree, and independent set. For example, we show that, for the shortest path problem, no algorithm in the FIXED priority model can achieve any approximation ratio (even one dependent on the graph size), but the well-known Dijkstra’s algorithm is an optimal ADAPTIVE priority algorithm. We also prove that the approximation ratio for weighted vertex cover achievable by ADAPTIVE priority algorithms is exactly 2. Here, a new lower bound matches the known upper bounds (Johnson in J. Comput. Syst. Sci. 9(3):256–278, 1974). We give a number of other lower bounds for priority algorithms, as well as a new approximation algorithm for minimum Steiner tree problem with weights in the interval [1,2]. S. Davis’ research supported by NSF grants CCR-0098197, CCR-0313241, and CCR-0515332. Views expressed are not endorsed by the NSF. R. Impagliazzo’s research supported by NSF grant CCR-0098197, CCR-0313241, and CCR-0515332. Views expressed are not endorsed by the NSF. Some work done while at the Institute for Advanced Study, supported by the State of New Jersey.     

Priority algorithms for graph optimization problems

We continue the study of priority or “greedy-like” algorithms as initiated in Borodin et al. (2003) [10] and as extended to graph theoretic problems in Davis and Impagliazzo (2009) [12]. Graph theoretic problems pose some modeling problems that did not exist in the original applications of Borodin et al. and Angelopoulos and Borodin (2002) [3]. Following the work of Davis and Impagliazzo, we further clarify these concepts. In the graph theoretic setting, there are several natural input formulations for a given problem and we show that priority algorithm bounds in general depend on the input formulation. We study a variety of graph problems in the context of arbitrary and restricted priority models corresponding to known “greedy algorithms”.     

The Power of Priority Algorithms for Facility Location and Set Cover

We apply and extend the priority algorithm framework introduced by Borodin, Nielsen, and Rackoff to define greedy-like algorithms for the (uncapacitated) facility location problems and set cover problems. These problems have been the focus of extensive research from the point of view of approximation algorithms and for both problems greedy-like algorithms have been proposed and analyzed. The priority algorithm definitions are general enough to capture a broad class of algorithms that can be characterized as greedy-like while still possible to derive non-trivial lower bounds on the approximability of the problems by algorithms in such a class. Our results are orthogonal to complexity considerations, and hence apply to algorithms that are not necessarily polynomial time.     

基于固定优先级和贪心法的航班时隙分配算法

航班时隙分配在空中交通管理领域中有着重要应用,考虑到在相同的延误时间情况下,不同类型的航班和不同的载客人数造成的综合损失差异,提出一种基于贪心法的航班分配算法。该算法在对航班进行排序的时候,在考虑到航空公司公平性的基础上,根据航班类型和载客数量,计算每架航班的优先级,然后根据当前可用时隙,以贪心法的规则找出优先级最高的航班,若有多个航班满足条件,则根据先来先服务原则进行选择,从而使经济损失和人员延误损失二者构成的综合损失最小化。算法仿真结果显示：该算法在很大程度上改进机场的运营效率,确保航空公司航班分配的公平性,维护航空公司及其服务对象的利益,具有一定的实用性和有效性。     

无人机平台非对称广播链路的动态优先权调度算法

战场数据分发系统需要传输不同长度的信息和数据,数据容量相差很大,采用动态优先权调度算法在系统平均延时、长短信息传输的公平性两个方面可以同时达到很好的性能。该调度算法适合于有优先级控制的广播链路。     

并发系统中基于优先级的调度分析

当前复杂的并发系统多采用模块化、逐步求精和信息隐藏等非形式化的原则来指导系统的开发,而这些指导原则抽象且无法保证分解系统的正确性。为此,对基于优先级控制的系统分解方法展开研究,提出一种系统分解的方法,并在理论上证明该分解方法的正确性。首先采用基于事件的行为模型对系统进行建模;接着定义调度、调度策略和调度策略正确性的概念;然后研究调度策略的分解方法,并证明了调度策略分解方法的正确性;最后根据该方法,开发出一种支持依赖模型建模和调度策略分解的原型工具,通过实例的演示,说明了使用该方法可以把系统分解成若干个子系统,从而设计出正确和有效的调度策略,以达到正确分解系统的目的。     

BubbleSearch: A simple heuristic for improving priority-based greedy algorithms

We introduce BubbleSearch, a general approach for extending priority-based greedy heuristics. Following the framework recently developed by Borodin et al., we consider priority algorithms, which sequentially assign values to elements in some fixed or adaptively determined order. BubbleSearch extends priority algorithms by selectively considering additional orders near an initial good ordering. While many notions of nearness are possible, we explore algorithms based on the Kendall-tau distance (also known as the BubbleSort distance) between permutations. Our contribution is to elucidate the BubbleSearch paradigm and experimentally demonstrate its effectiveness.     

Approximation Algorithms for Average Stretch Scheduling

We study the basic problem of preemptive scheduling of a stream of jobs on a single processor. Consider an on-line stream of jobs, and let the ith job arrive at time r(i) and have processing time p(i). If C(i) is the completion time of job i, then the flow time of i is C(i) − r(i) and the stretch of i is the ratio of its flow time to its processing time; that is, . Flow time measures the time that a job is in the system regardless of the service it requests; the stretch measure relies on the intuition that a job that requires a long service time must be prepared to wait longer than jobs that require small service times. We present the improved algorithmic results for the average stretch metric in preemptive uniprocessor scheduling. Our first result is an off-line polynomial-time approximation scheme (PTAS) for average stretch scheduling. This improves upon the 2-approximation achieved by the on-line algorithm srpt that always schedules a job with the shortest remaining processing time. In a recent work, Chekuri and Khanna (Proc. 34th Ann. Symp. Theory Comput., 297–305, 2002) have presented approximation algorithms for weighted flow time, which is a more general metric than average stretch; their result also yields a PTAS for average stretch. Our second set of results considers the impact of incomplete knowledge of job sizes on the performance of on-line scheduling algorithms. We show that a constant-factor competitive ratio for average stretch is achievable even if the processing times (or remaining processing times) of jobs are known only to within a constant factor of accuracy.     

无线调度算法

为满足无线应用中的Qos要求,调度算法是很重要的。由于无线网络变化的链路错误率和容量,因此为其设计调度算法非常有挑战性。近来提出了多种适合无线网络的调度算法。该文分析了3种基于TDD的调度算法。讨论了各种算法的实现过程和优缺点,最后对它们的性能进行比较．得出了有意义的结论。     

基于优先级的Three-Queue调度算法研究

针对Hadoop平台上调度算法存在的不足,提出了一种改进的调度算法———Triple-Queue算法。在充分考虑数据的本地性后,Triple-Queue算法设计了一种改进的优先级计算模型,以有效地区分用户作业的等级,同时又保证一定程度的公平性,进而减小作业执行时间,避免系统资源浪费。实验结果表明,随着数据量的提高,该算法执行效率明显提高,同时能够较好地解决数据本地性问题。     

无人机中继通信系统中信息传输调度算法研究

研究了将无人机作为通信中继平台对战区实施无线通信覆盖时的信息传输调度算法.首先介绍了几种基于信息特征(如优先级、长度、信息在系统总的占用时间等)的调度算法.为了克服传统调度算法的缺点,提出了一种改进的动态优先权调度(DPS,Dynamic Priority Scheduling)算法,将信息的优先级与接受系统服务的时间联系起来,动态调整信息的优先权,从而获得较小的系统平均时延,而且对不同信息又不失“公平性“.最后给出了几种调度算法的仿真结果,并对结果进行了分析.分析表明,动态优先权调度算法是一种比较适合无人机通信中继的实用调度算法.     

Algorithms for Minimizing Response Time in Broadcast Scheduling

In this paper we study the following problem. There are n pages which clients can request at any time. The arrival times of requests for pages are known in advance. Several requests for the same page may arrive at different times. There is a server that needs to compute a good broadcast schedule. Outputting a page satisfies all outstanding requests for the page. The goal is to minimize the average waiting time of a client. This problem has recently been shown to be NP-hard. For any fixed , 0 < \le &frac;, we give a 1/-speed, polynomial time algorithm with an approximation ratio of 1/(1 – ). For example, setting = &frac; gives a 2-speed, 2-approximation algorithm. In addition, we give a 4-speed, 1-approximation algorithm improving the previous bound of 6-speed, 1-approximation algorithm.     

扩展概念格的渐进式构造

鉴于已在Galois格的基础上提出了扩展概念格,文章对已经构造好的扩展概念格,在数据对象增加时如何更新的问题,提出了一种渐进式构造算法,经验证它是一个有效的算法。     

基于贪婪算法成像侦察卫星调度方法研究

成像侦察卫星的调度问题需要考虑大量互相联系的约束条件,实现全面调度的难度比较大,特别是在作战的情况下,很难满足快速战略决策的要求,而且各种干扰因素将会对卫星的状态产生影响,需要优越的初始调度方案作为基础.针对以上提出的实际问题,首先对成像侦查卫星约束条件进行分析,在简单假设的基础上对问题进行描述,建立卫星调度的约束模型,基于贪婪算法原理,通过软件实现调度模型求解,得到成像侦查卫星的快速调度方案,为卫星任务状态变化的二次调度和满足快速战略决策提供比较令人满意的调度基础解.     

Simple On-Line Algorithms for the Maximum Disjoint Paths Problem

In this paper we study the classical problem of finding disjoint paths in graphs. This problem has been studied by a number of authors both for specific graphs and general classes of graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitiveness of on-line algorithms, not much is known about how well on-line algorithms can perform in the general setting. The best results obtained so far use the expansion of a network to measure the algorithms performance. We use a different parameter called the routing number that, as we will show, allows more precise results than the expansion. It enables us to prove tight upper and lower bounds for deterministic on-line algorithms. The upper bound is obtained by surprisingly simple greedy-like algorithms. Interestingly, our upper bound on the competitive ratio is even better than the best previous approximation ratio for off-line algorithms. Furthermore, we introduce a refined variant of the routing number and show that this variant allows us, for some classes of graphs, to construct on-line algorithms with a competitive ratio significantly below the best possible upper bound that could be obtained using the routing number or the expansion of a network only. We also show that our on-line algorithms can be transformed into efficient algorithms for the more general unsplittable flow problem.     

Ordinal Priority Approach (OPA) in Multiple Attribute Decision-Making

The current study aims to present a new method called Ordinal Priority Approach (OPA) in Multiple Attribute Decision-Making (MADM). This method can be used in individual or group decision-making (GDM). In the case of GDM, through this method, we first determine the experts and their priorities. The priority of experts may be determined based on their experience and/or knowledge. After prioritization of the experts, the attributes are prioritized by each expert. Meanwhile, each expert ranks the alternatives based on each attribute, and the sub-attributes if any. Ultimately, by solving the presented linear programming model of this method, the weights of the attributes, alternatives, experts, and sub-attributes would be obtained simultaneously. A significant advantage of the proposed method is that it does not make use of pairwise comparison matrix, decision-making matrix (no need for numerical input), normalization methods, averaging methods for aggregating the opinions of experts (in GDM) and linguistic variables. Another advantage of this method is the possibility for experts to only comment on the attributes and alternatives for which they have sufficient knowledge and experience. The validity of the proposed model has been evaluated using several group and individual instances. Finally, the proposed method has been compared with other methods such as AHP, BWM, TOPSIS, VIKOR, PROMETHEE and QUALIFLEX. Based on comparisons among the weights and ranks using Spearman and Pearson correlation coefficients, the proposed method has an applicable performance compared with other methods.     

优先级顶协议的形式化验证

优先级顶协议是一种优先级驱动的抢占式调度协议,它具有无死锁和单阻塞的性质.Dang Van Hung 和Philip Chan在文献[6]中形式地规范和验证了这两个性质.但他们没有对状态函数HiPripcp明确定义,这使得验证的细节较难理解.为了解决这个问题,提出了一种新的方法来验证优先级顶协议单阻塞的性质.通过时段演算的方法,对优先级顶协议进行了规范,并给出了状态函数HiPripcp的明确定义.根据优先级顶协议的规范,形式地验证了该协议的单阻塞性质.采用的验证方法更少地依赖于HiPripcp,这使得验证的细节更易于理解.此外,提出的验证方法可被应用于实时数据库系统中类似协议的形式化验证.     

Algorithms for Fuzzy Segmentation

Fuzzy segmentation is an effective way of segmenting out objects in pictures containing both random noise and shading. This is illustrated both on mathematically created pictures and on some obtained from medical imaging. A theory of fuzzy segmentation is presented. To perform fuzzy segmentation, a ‘connectedness map’ needs to be produced. It is demonstrated that greedy algorithms for creating such a connectedness map are faster than the previously used dynamic programming technique. Once the connectedness map is created, segmentation is completed by a simple thresholding of the connectedness map. This approach is efficacious in instances where simple thresholding of the original picture fails. Received: 22 October 1998?Received in revised form: 22 November 1998?Accepted: 2 December 1998     

异构集群环境下负载平衡调度算法研究与实现

围绕平衡负载这一目标,针对进程级并行任务的动态调度问题进行了研究,提出了一个异构集群环境下动态负载平衡算法,它结合了自适应数据采集与交换算法,有效的解决了服务器之间负载不平衡的问题,提高了系统的吞吐率。