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University of California – San Diego

1. Moeller, Daniel Paul. Exploiting Structure in the Stable Matching Problem.

Degree: Computer Science, 2016, University of California – San Diego

Stable matching is a widely studied problem in social choice theory. For the basiccentralized case, an optimal quadratic time algorithm is known. However, we presentseveral notions of structure and use them to provide tighter convergence bounds andfaster stable matching algorithms for structured instances.First, we consider the decentralized case, where several natural randomizedalgorithmic models for this setting have been proposed that have worst case exponentialtime in expectation. We describe a novel structure associated with a stable matching ona matching market. Using this structure, we are able to provide a finer analysis of the complexity of a subclass of decentralized matching markets.We then study the centralized stable matching problem when the preferencelists are not given explicitly but are represented in a succinct way. We ask whetherthe problem becomes computationally easier and investigate other implications of thisstructure. We give subquadratic algorithms for finding a stable matching in special casesof natural succinct representations of the problem, the d-attribute, d-list, geometric, andsingle-peaked models. We also present algorithms for verifying a stable matching in thesame models. We further show that for d = w(logn) both finding and verifying a stablematching in the d-attribute and d-dimensional geometric models requires quadratic timeassuming the Strong Exponential Time Hypothesis. These models are therefore as hardas the general case for large enough values of d.

Subjects/Keywords: Computer science; Complexity; Decentralized; Jealousy Graph; Stable Matching; Structure; Succinct

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Moeller, D. P. (2016). Exploiting Structure in the Stable Matching Problem. (Thesis). University of California – San Diego. Retrieved from http://www.escholarship.org/uc/item/6f80v7jc

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Moeller, Daniel Paul. “Exploiting Structure in the Stable Matching Problem.” 2016. Thesis, University of California – San Diego. Accessed December 11, 2019. http://www.escholarship.org/uc/item/6f80v7jc.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Moeller, Daniel Paul. “Exploiting Structure in the Stable Matching Problem.” 2016. Web. 11 Dec 2019.

Vancouver:

Moeller DP. Exploiting Structure in the Stable Matching Problem. [Internet] [Thesis]. University of California – San Diego; 2016. [cited 2019 Dec 11]. Available from: http://www.escholarship.org/uc/item/6f80v7jc.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Moeller DP. Exploiting Structure in the Stable Matching Problem. [Thesis]. University of California – San Diego; 2016. Available from: http://www.escholarship.org/uc/item/6f80v7jc

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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