Online Algorithms for Fair Allocation of Goods

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Eftekhari Hesari, Mahsa | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49909 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Zarrabi Zadeh, Hamid
Abstract:
In this thesis, we study the max-min fair allocation of goods which represents one of the most basic problems in scheduling theory. Here we consider the online problem of allocating a set of indivisible items among agents whom each has her own preference list over the items. The goal is to maximize the minimum happiness (profit) of the agents.We present an algorithm with competitive ratio n 2 and prove that this competitive ratio is tight. We also consider this problem when each agent has a type and the number of types is constant and solve the problem where the number of types is 2 or 3. Furthermore, we study the problem with resource augmentation. We focus on doubling the number of items and prove that any deterministic algorithms will have a linear competitive ratio even with resource augmentation. We conclude this work by presenting an optimal algorithm with log n copies of each item
Keywords:
Competetive Ratio ; Online Algorithm ; Goods Allocation ; Bottlenck Matching