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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 53238 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Foroughmand Aarabi, Mohammad Hadi
- Abstract:
- Online problems were first introduced in 1980s due to process the data arise from the internet. An Online algorithm is an algorithm which takes a part of input at each step and should give an irrevocable answer before entrance of the rest of data. Online problems are considered when the size of the input is substantial or there are time limitations to wait for the whole input to arrive. One of the first online algorithms discussed was the online bipartite matching. In this problem there exists a bipartite graph with one offline part which is present from the beginning and nodes of the other part entering one by one with all of their corresponding edges. At the entrance of each node the algorithm should decide which neighbor to match with or to leave the node unmatched. The goal is to obtain a maximum size matching at the end. The main application of the problem is internet advertising although it can be used whenever a matching between parties from two categories are sought. In this thesis we study the online matching in bipartite graphs. First we outline the problem and its different arrival models and some of its variations which were defined to model different real-life applications. Then we describe some of the algorithms designed for different input models of online bipartite matching and explain one of the important technics used for competitive analysis of the algorithms. At the end we examine the algorithms on different datasets and analyze their competitive ratios
- Keywords:
- Bipartite Graph ; Randomized Algorithm ; Competitive Analysis ; Online Algorithm ; Matching Algorithms
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