stable matching
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2022 ◽  
Vol 32 (3) ◽  
pp. 1831-1842
Author(s):  
Liang Dai ◽  
AoSong He ◽  
Guang Sun ◽  
Yuxing Pan

2021 ◽  
Vol 9 (4) ◽  
pp. 1-14
Author(s):  
Simon Mauras

Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal work by Gale and Shapley. When the input preference profile is generated from a distribution, we study the output distribution of two stable matching procedures: women-proposing-deferred-acceptance and men-proposing-deferred-acceptance. We show that the two procedures are ex-ante equivalent—that is, under certain conditions on the input distribution, their output distributions are identical. In terms of technical contributions, we generalize (to the non-uniform case) an integral formula, due to Knuth and Pittel, which gives the probability that a fixed matching is stable. Using an inclusion-exclusion principle on the set of rotations, we give a new formula that gives the probability that a fixed matching is the women/men-optimal stable matching.


2021 ◽  
pp. 1-19
Author(s):  
Huagang Tong ◽  
Jianjun Zhu ◽  
Yang Yi

Sharing economy is significant for economic development, stable matching plays an essential role in sharing economy, but the large-scale sharing platform increases the difficulties of stable matching. We proposed a two-sided gaming model based on probabilistic linguistic term sets to address the problem. Firstly, in previous studies, the mutual assessment is used to obtain the preferences of individuals in large-scale matching, but the procedure is time-consuming. We use probabilistic linguistic term sets to present the preferences based on the historical data instead of time-consuming assessment. Then, to generate the satisfaction based on the preference, we regard the similarity between the expected preferences and actual preferences as the satisfaction. Considering the distribution features of probabilistic linguistic term sets, we design a shape-distance-based method to measure the similarity. After that, the previous studies aimed to maximize the total satisfaction in matching, but the individuals’ requirements are neglected, resulting in a weak matching result. We establish the two-sided gaming matching model from the perspectives of individuals based on the game theory. Meanwhile, we also study the competition from other platforms. Meanwhile, considering the importance of the high total satisfaction, we balance the total satisfaction and the personal requirements in the matching model. We also prove the solution of the matching model is the equilibrium solution. Finally, to verify the study, we use the experiment to illustrate the advantages of our study.


2021 ◽  
Vol 13 (22) ◽  
pp. 4637
Author(s):  
Runzhi Jiao ◽  
Qingsong Wang ◽  
Tao Lai ◽  
Haifeng Huang

The dramatic undulations of a mountainous terrain will introduce large geometric distortions in each Synthetic Aperture Radar (SAR) image with different look angles, resulting in a poor registration performance. To this end, this paper proposes a multi-hypothesis topological isomorphism matching method for SAR images with large geometric distortions. The method includes the Ridge-Line Keypoint Detection (RLKD) and Multi-Hypothesis Topological Isomorphism Matching (MHTIM). Firstly, based on the analysis of the ridge structure, a ridge keypoint detection module and a keypoint similarity description method are designed, which aim to quickly produce a small number of stable matching keypoint pairs under large look angle differences and large terrain undulations. The keypoint pairs are further fed into the MHTIM module. Subsequently, the MHTIM method is proposed, which uses the stability and isomorphism of the topological structure of the keypoint set under different perspectives to generate a variety of matching hypotheses, and iteratively achieves the keypoint matching. This method uses both local and global geometric relationships between two keypoints, hence it achieving better performance compared with traditional methods. We tested our approach on both simulated and real mountain SAR images with different look angles and different elevation ranges. The experimental results demonstrate the effectiveness and stable matching performance of our approach.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yujie Zheng ◽  
Meiyan Li ◽  
Jiakun Liu

To improve the satisfaction of both service demanders (SDs) and service providers (SPs) in the matching of cloud manufacturing (CMfg) tasks and services, a two-sided stable matching model of CMfg tasks and service considering the nonlinear relationship between satisfaction and expectations is proposed. As the expectations of SDs and SPs are difficult to be quantified directly, an evaluation method based on interval-valued hesitant fuzzy linguistic sets (IVHFLSs) is first presented. Next, a nonlinear model of satisfaction and expectations is built to quantify the satisfaction, which achieves accurate quantification of satisfaction. Then, a two-sided stable matching model of CMfg tasks and service is built, which takes the satisfaction of SDs and SPs as the optimization goals and considers the individual rationalities and blocking pairs. Finally, an adaptive genetic algorithm (AGA) is designed to solve the proposed two-sided matching model. A practical application and comparison analysis is used to verify the effectiveness and superiority of the research.


Author(s):  
Zhixue Wang ◽  
Hanning Chen ◽  
Xiaodan Liang ◽  
Maowei He
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