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Optimal bundles for sponsored search auctions via bracketing scheme

Frontiers of Computer Science 2019年第2期13卷 333-342页

作者： Zheng-Dong XIA Tian-Ming BU Wen-Hui GONG Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai 200233 China

Sponsored search auction has been recently studied and auctioneer's revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method. We prove that finding a bracketing scheme that maximizes the auctioneer's revenue is strongly np-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with Kanonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both np-hard.

关键词： sponsored search auction revenue maximization bracketing scheme np-hardness

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hardness and Methods to Solve CLIQUE

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Journal of Computer Science & Technology 2001年第4期16卷 388-391页

作者：朱大铭栾峻峰马绍汉 Department of Computer Science Shandong University Jinan P.R. China

The paper briefly reviews np-hard optimization problems and their inapproximability. The hardness of solving CLIQUE problem is specifically dis- cussed. A dynamic-programming algorithm and its improved version for CLIQUE are reviewed and some additional analysis is presented. The analysis implies that the improved algorithm, HEWN (hierarchical edge-weighted network), only provides a heuristic or useful method, but cannot be called a polynomial algorithm.

关键词： algorithm np-hardness approximation ratio dynamic programming complexity

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On the Complexity of Finding Tensor Ranks

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Communications on Applied Mathematics and Computation 2021年第2期3卷 281-289页

作者： Mohsen Aliabadi Shmuel Friedland Department of Mathematics Iowa State University411 Morrill RoadAmesIA 50011-2104USA Department of Mathematics Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoIL 60607-7045USA

The purpose of this note is to give a linear algebra algorithm to find out if a rank of a given tensor over a field F is at most k over the algebraic closure of F,where K is a given positive *** estimate the arithmeti... 详细信息

关键词： Gauss elimination Homogeneous polynomial np-hardness Symmetric tensor Tensor rank

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A QUASI-PHYSICAL METHOD FOR SOLVING THE SCHEDULING PROBLEM OF SPACE UTILIZATION

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Science China Mathematics 1991年第9期34卷 1144-1152页

作者：刘炯朗黄文奇陈亮 Department of Computer Science University of Illinois Urbana-Champaign U.S.A. Department of Computer Science Huazhong University of Science and Technology Wuhan 430074 PRC

The scheduling of space utilization can be regarded as a packing problem in 4-dimensionaltime-space while for the packing problem in 3-dimensional space there is already a meth-od for solution of a quasi-physical type. A quasi-physical method for solving the schedulingproblem is obtained after proper extension of this method. It may be developed into anexpert system or CAD software system for the scheduling of space utilization of great signif-icance.

关键词： np-hardness packing problem scheduling problem.

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On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods

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International Journal of Communications, Network and System Sciences 2012年第11期5卷 774-784页

作者： Mohamed Askali Ahmed Azouaoui Said Nouh Mostafa Belkasmi SIME Lab National School of Computer Science and Systems Analysis(ENSIAS)Mohammed V-Souisi UniversityRabatMorocco

The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.

关键词： Minimum Distance Error Impulse Method Heuristic Methods Genetic Algorithms np-hardness Linear Error Correcting Codes BCH Codes QR Codes Double Circulant Codes

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