Near optimal algorithms for online weighted bipartite matching in adversary model

doi:10.1007/s10878-016-0100-2

	Near optimal algorithms for online weighted bipartite matching in adversary model
	Sun, Xiaoming 1,2; Zhang, Jia 1,2; Zhang, Jialin 1,2
	2017-10-01
发表期刊	JOURNAL OF COMBINATORIAL OPTIMIZATION
ISSN	1382-6905
卷号	34 期号:3 页码:689-705
摘要	Bipartite matching is an important problem in graph theory. With the prosperity of electronic commerce, such as online auction and AdWords allocation, bipartite matching problem has been extensively studied under online circumstances. In this work, we study the online weighted bipartite matching problem in adversary model, that is, there is a weighted bipartite graph and the left side L is known as input, while the vertices in R come one by one in an order arranged by the adversary. When each vertex in R comes, its adjacent edges and relative weights are revealed. The algorithm should irreversibly decide whether to match this vertex to an unmatched neighbor in L with the objective to maximize the total weight of the obtained matching. When the weights are unbounded, the best algorithm can only achieve a competitive ratio , where n is the number of vertices coming online. Thus, we mainly deal with two variants: the bounded weight problem in which all weights are in the range , and the normalized summation problem in which each vertex in one side has the same total weights. We design algorithms for both variants with competitive ratio and respectively. Furthermore, we show these two competitive ratios are tight by providing the corresponding hardness results.
关键词	Online matching Weighted bipartite graph Adversary model Near optimal algorithm
DOI	10.1007/s10878-016-0100-2
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[61222202] ; National Natural Science Foundation of China[61433014] ; National Natural Science Foundation of China[61502449] ; National Natural Science Foundation of China[61602440] ; 973 Program of China[2016YFB1000201] ; China National Program for support of Top-notch Young Professionals
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Interdisciplinary Applications ; Mathematics, Applied
WOS记录号	WOS:000411586300003
出版者	SPRINGER
引用统计	被引频次：4[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/6775
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Zhang, Jia
作者单位	1.Chinese Acad Sci, Inst Comp Technol, CAS Key Lab Network Data Sci & Technol, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Sun, Xiaoming,Zhang, Jia,Zhang, Jialin. Near optimal algorithms for online weighted bipartite matching in adversary model[J]. JOURNAL OF COMBINATORIAL OPTIMIZATION,2017,34(3):689-705.
APA	Sun, Xiaoming,Zhang, Jia,&Zhang, Jialin.(2017).Near optimal algorithms for online weighted bipartite matching in adversary model.JOURNAL OF COMBINATORIAL OPTIMIZATION,34(3),689-705.
MLA	Sun, Xiaoming,et al."Near optimal algorithms for online weighted bipartite matching in adversary model".JOURNAL OF COMBINATORIAL OPTIMIZATION 34.3(2017):689-705.