Studying the Problem of Maximum Matching in Stochastic Environments

Please enable javascript in your browser.

Soheil, Farehe | 2022

431 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55010 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Ghodsi, Mohammad
Abstract:
The problem studied in this research is the online stochastic bipartite matching. In this problem the vertices of one side of the given graph arrive in an online manner, with respect to a probability distribution. Also the edges of the graph exist according to a given probability distribution and one should perform queries from an oracle to know about the existence of an edge. The given graph shall be weighted or unweighted. The goal here is to find a maximum matching in the graph that is as close to the omniscient optimum as possible, while the number of queries performed per vertex is limited. In the general case of the problem, there are no specific conditions, but in other versions, restrictions on the number of queries performed per online vertex and the manner of performing queries are mentioned, which add to the difficulty of providing a solution. The main purpose of this research is to study this problem as well as to examine the difficulties and obstacles in solving it. Improving the proposed approximation algorithms and the complexity of their queries are the other motives of this research.
Keywords:
Optimization ; Online Algorithm ; Approximate Algorithm ; Random Graph ; Maximum Matching