Sharif Digital Repository

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... 

Simulation has numerous applications, for instance in training. Training for different types of surgery with the use of simulation is very common today. During the surgery, the surgeon tears and cuts fine tissues. Modeling this process has always been one of the most challenging areas in the field of simulation design. Triangular meshing, especially Delaunay triangulation is often used to simulate a twodimensional surface. Now, if we want to simulate the process of cutting that surface, we need to modify the mesh in a real-time manner and simulate the cutting process by adding, removing, or changing the vertices, edges and triangles. therefore, to re-design the mesh according to the cut, we... 

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,... 

Energy Harvesting has been appeared as an approach in order to make the green communications possible. In Energy Harvesting systems, nodes extract energy from the nature to extend their lifetimes. The harvested energy can also be used for the purpose of communication and specially for the transmission process. Compared to the conventional batterypowered systems, the Energy Harvesting systems have access to an unbounded source of energy (like vibration absorption devices, water mills, wind turbines, microbial fuel cells, solar cells, thermo-electric generators, piezoelectric cells, etc). However, the diffused nature of this energy makes it difficult to be used for communication. In this work,... 

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... 

In this research, the problem of path planning for simple robots is studied. The robot used in this study is a robot that can only detect the order of discontinuities in depth information (gaps). Former problems that have been studied so far for this type of robot are path planning and searching in street polygons. Street polygons are a type of simple polygons such that if a robot starts from a specific starting point on the street, pointing to the end of the street at another specific point, it has seen the whole area of the polygon. The main purpose of this research is to study the environment features and finding the algorithms for path planning in streets in general modes including... 

Payment channel networks (PCNs) are a promising technology to improve the scalability of cryptocurrencies. Users can send instant and almost free transactions via payment channel networks and, at the same time, enjoy the security guarantees of Blockchains. In order to open a mutual payment channel, two users should send a ``channel creation" transaction to the underlying Blockchain. Through this transaction, two parties deposit some money on the Blockchain. This money, which we call the channel's capacity, can be used to send off-chain transactions between the two users. After the channel creation, the channel-holders can send each other off-chain transactions by forwarding the money back... 

In this research, path planning in unknown environment is considered. It is assumed that the robot’s sensors are the only tools to collect information from the scene. Volume of the information gathered from the environment depends on the capability of the sensor. So, a detour from the optimal path is unavoidable. In this research, the basic robot is equipped with a minimal sensing system that only detects the iscontinuities in depth information (gaps). We present some online search strategies that guide such a robot to navigate unknown streets from a start point s to reach a target point t. Then, we empower the robot by adding a compass to patrol more general classes of polygons. We present...