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approximation of dense-n/2-subgraph and table compression problems

Science China Mathematics 2005年第9期48卷 1223-1233页

作者： XU Dachuan~1 HAN Jiye~2 & DU Dongle~3 1. College of Applied Sciences,Beijing University of Technology,Beijing 100022,China 2. Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China 3. Faculty of Administration,University of New Brunswick,P.O.Box 4400,Fredericton,NB E3B 5A3,Canada College of Applied Sciences Beijing University of Technology Beijing 100022 China Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Faculty of Administration University of New Brunswick P.O. Box 4400 Fredericton NB E3B 5A3 Canada

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2-subgraph and table compression. Based on SDP relaxation and advanced rounding techniques, we first propose 0.5982 and 0.5970-approximation algorithms respectively for the dense-n/2-subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0.6243 and 0.6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP relaxation. The results for TCP beat the 0.5 bound of a simple greedy algorithm on this problem, and hence answer an open question of Anderson in an affirmative way.

关键词： dense-n/2-subgraph problem(DSP) table compression problem(TCP) SDP approximation ratio

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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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approximation Algorithms for Discrete Polynomial Optimization

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Journal of the Operations Research Society of China 2013年第1期1卷 3-36页

作者： Simai He Zhening Li Shuzhong Zhang Department of Management Sciences City University of Hong KongKowloonHong Kong Department of Mathematics Shanghai UniversityShanghai 200444China Department of Industrial&Systems Engineering University of MinnesotaMinneapolisMN 55455USA

In this paper,we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete(typically binary)*** models have natural applications in graph theory,neural networks,error-correcting codes,among many *** particular,we focus on three types of optimization models:(1)maximizing a homogeneous polynomial function in binary variables;(2)maximizing a homogeneous polynomial function in binary variables,mixed with variables under spherical constraints;(3)maximizing an inhomogeneous polynomial function in binary *** propose polynomial-time randomized approximation algorithms for such polynomial optimizationmodels,and establish the approximation ratios(or relative approximation ratios whenever appropriate)for the proposed *** examples of applications for these models and algorithms are discussed as well.

关键词： Polynomial optimization problem Binary integer programming Mixed integer programming approximation algorithm approximation ratio

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