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1.
示例学习的扩张矩阵理论 总被引:30,自引:2,他引:28
本文提出示例学习的一种计算理论,扩张矩阵论.根据这个理论,示例学习中一些主要最优化问题被证明是NP难题,并给出这些难题的近似解法及下界的估计. 相似文献
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We study the complexity issues for Walrasian equilibrium in a special case of combinatorial auction, called single-minded
auction, in which every participant is interested in only one subset of commodities. Chen et al. (J. Comput. Syst. Sci. 69(4):
675–687, 2004) showed that it is NP-hard to decide the existence of a Walrasian equilibrium for a single-minded auction and proposed a
notion of approximate Walrasian equilibrium called relaxed Walrasian equilibrium. We show that every single-minded auction
has a relaxed Walrasian equilibrium that satisfies at least two-thirds of the participants, proving a conjecture posed in
Chen et al. (J. Comput. Syst. Sci. 69(4): 675–687, 2004). Motivated by practical considerations, we introduce another concept of approximate Walrasian equilibrium called weak Walrasian
equilibrium. We show NP-completeness and hardness of approximation results for weak Walrasian equilibria.
In search of positive results, we restrict our attention to the tollbooth problem (Guruswami et al. in Proceedings of the
Symposium on Discrete Algorithms (SODA), pp. 1164–1173, 2005), where every participant is interested in a single path in some underlying graph. We give a polynomial time algorithm to
determine the existence of a Walrasian equilibrium and compute one (if it exists), when the graph is a tree. However, the
problem is still NP-hard for general graphs. 相似文献
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We excavate the wisdom from an old Chinese proverb “gold corner, silver side and strawy void”, and further improve it into
“maximum value in diamond cave” for solving the NP-hard cuboid packing problem. We extract, integrate and formalize the idea
by west modern mathematical tools, and propose a pure quasi-human algorithm. The performance of the algorithm is evaluated
on two sets of public benchmarks. For 100 strongly heterogeneous difficult benchmarks, experiments show an average packing
utilization of 87.31%, which surpasses current best record reported in the literature by 1.83%. For 47 difficult benchmarks
without orientation constraint, experiments show an average volume utilization of 92.05%, which improves current best record
reported in the literature by 1.05%.
Supported by the National Natural Science Foundation of China (Grant No. 60773194), the National Basic Research Program of
China (Grant No. 2004CB318000), and Postdoctoral Science Foundation of China (Grant No. 20070420174) 相似文献
5.
介绍了一种基于复制结点的消除线路交叉的模型.该模型提出了一个优化问题,就是最小化结点复制的数量.同时提出一个自定义问题——"最大简单共享问题",并证明最小化结点复制的数量与最大共享问题是等价的.证明了最大简单共享问题是NP-hard的,给出了一种简单的贪心算法,并证明该贪心算法的近似度为3.引入一个"最大互斥简单共享问题",该问题是最大简单共享问题的2-近似.将其转化为在一系列图上的完美匹配问题,使该问题可以在多项式时间内得到完美解决.最后,在最大互斥简单共享的基础上,用局部搜索的方法将近似度提高到12/7. 相似文献
6.
TSP问题的脂肪计算复杂性与启发式算法设计 总被引:2,自引:0,他引:2
旅行商问题(traveling salesman problem,简称TSP)是经典的NP-难解组合优化问题之一,求解它的高效启发式算法一直是计算机科学研究的热点.脂肪作为描述TSP结构特征的新工具,对启发式算法设计具有重要意义.目前,TSP问题的脂肪研究还处于初始阶段,缺乏理论分析结果及相关的启发式算法.首先分析了TSP问题的脂肪计算复杂性,通过构造偏移实例的技巧,证明了获取TSP的脂肪是NP-难解的,即在P(NP的假设下,不存在算法可以在多项式时间内获得完整脂肪.在此基础上,通过分析TSP问题局部最优解与脂肪的关系,给出了求解TSP问题的元启发式算法--动态候选集搜索(dynamic candidate set search,简称DCSS)算法.利用该算法,改进了目前求解TSP问题最好算法之一的LKH.TSPLIB典型实例的实验结果表明,改进后的算法在解的质量上有较为明显的提高.新的基于脂肪的启发式算法对于求解其他NP-难解问题具有一定的参考价值. 相似文献
7.
Cops and Robbers is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robbers, distance k Cops and Robbers, where the cops win if at least one of them is of distance at most k from the robber in G. The cop number of a graph G is the minimum number of cops needed to capture the robber in G. The distance k analogue of the cop number, written ck(G), equals the minimum number of cops needed to win at a given distance k. We study the parameter ck from algorithmic, structural, and probabilistic perspectives. We supply a classification result for graphs with bounded ck(G) values and develop an O(n2s+3) algorithm for determining if ck(G)≤s for s fixed. We prove that if s is not fixed, then computing ck(G) is NP-hard. Upper and lower bounds are found for ck(G) in terms of the order of G. We prove that
8.
As the hot line in NP-hard problems research in recent years, backbone analysis is crucial for phase transition, hardness, and algorithm design. Whereas theoretical analysis of backbone and its applications in algorithm design are still at a begin- ning state yet, this paper took the quadratic assignment problem (QAP) as a case study and proved by theoretical analysis that it is NP-hard to find the backbone, i.e., no algorithm exists to obtain the backbone of a QAP in polynomial time. Results of this paper showed that it is reasonable to acquire approximate backbone by inter- section of local optimal solutions. Furthermore, with the method of constructing biased instances, this paper proposed a new meta-heuristic -- biased instance based approximate backbone (BI-AB), whose basic idea is as follows: firstly, construct a new biased instance for every QAP instance (the optimal solution of the new instance is also optimal for the original one); secondly, the approximate backbone is obtained by intersection of multiple local optimal solutions computed by some existing algorithm; finally, search for the optimal solutions in the reduced space by fixing the approximate backbone. Work of the paper enhanced the research area of theoretical analysis of backbone. The meta-heuristic proposed in this paper provided a new way for general algorithm design of NP-hard problems as well. 相似文献
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The inventory, routing and scheduling decisions are three major driving factors for supply chain performance. Since they are related to one another in a supply chain, they should be determined simultaneously to improve the decision quality. In the past, the inventory policy, vehicle routing and vehicle scheduling are determined sequentially and separately. Hence, the total cost (inventory, routing and vehicle costs) would increase. In this paper, an integrated model for the inventory routing and scheduling problem (IRSP) is proposed. Since searching for the optimal solution for this model is a non-polynomial (NP) problem, a metaheuristic, variable neighborhood search (VNS), is proposed. The proposed method was compared with other existing methods. The experimental results indicate that the proposed method is better than other methods in terms of average cost per day. 相似文献