Sharif Digital Repository

In this thesis, we considered several types of the visibility problem. These problems include computing the visibility polygon of a point observer inside a polygonal domain, maintaining visibility polygon of a moving point observer, visibility coherence in space, maintaining visibility polygon of a moving segment observer and visibility dependent simplification. Furthermore, we considered these problems in both offline and streaming settings. These problems arise in different practical areas, such as computer graphics, machine vision, robotics, motion planning, geographic information systems (GIS) and computational geometry. We obtained effective theoretical results as well as superior... 

Nowadays binary sensors such as infrared sensors are vastly employed in industrial, commercial and general applications due to their simplicity and low price. Beam sensors are common type of these sensors which can detect objects when they cross its beam. Sequence of sensors which are crossed in a time order is called sensor word. Consider an object, produced sensor word shows the order which it has crossed the beams. If we have more than one object then sensor word is combination of all sensor words produced by all object. We need to separate each sensor word. In this research, sensor word is developed to Fixed-Charge Minimum Cost Maximum Flow Network type.In this case, the consequent... 

Recently, computer scientists and economists have defined many joint problems and cooperate widely in various areas. Importance of this interconnection is clear for everybody, now. New works have been conducted, nowadays, to use the daily - increasing web-based social networks in viral marketing for improving companies profits. The main problem which is proved to be NP-Complete in this context is about discovering k most influential nodes in a network. In this dissertation, we generalize the problem to a group-based version and we we use group-based advertising to achieve our main goal. A new algorithm called Group-Based Diffusion technique is proposed in this thesis for solving this problem... 

This thesis focuses on design of various strategies to maximize sellers’ profits in different social markets where agents’ behaviors and decisions are greatly influenced by their network friends. We introduce different social networks with various properties and present models to analyze the agents’ behaviors. We also study different pricing strategies for each model and design algorithms for sellers in order to maximize their profits. Furthermore, we study the prediction markets where agents with different points of views participate in the market. Each agent invests in the market with respect to her information. We propose a model for these markets which are both predictable and... 

We consider extending the visibility polygon of a given point q inside a simple polygon by converting one or some of the edges to mirrors. It is known that the visibility polygon of a point inside a polygon in the presence of a mirror can be computed in linear time. We propose a linear time algorithm that checks whether a given segment inside a simple polygon is visible by a given point q via a mirror-edge, and finds all such edges. And we prove that finding edges to add exactly k unit squares to the visibility polygon of a query point q in most cases is NP-complete and its minimization is NP-hard. These cases contain single and muliple, either with secular or difuse reflections. Moreover,... 

We consider a special class of Congestion Games enhanced with a notion of time.Network Routing problems, such as road traffic networks, computer neworks, and evacuation problems are some applications of this class of games. Two subclasses of these games, namely atomic and non-atomic is considered in this article, both of them introduced in 2009. Some of the existing results are Nash equilibria existence proof for “single-source single-sink” case, and a mechanism for improving price of anarchy in the non-atomic subclass. There are also some results in the atomic subclass of this game.We extend both models of atomic and non-atomic subclasses to “multi-source,multi-sink” configurations. We call... 

In many network which relationships between nodes are defined based on the similarity of attributes (Such as the World Wide Web and social networks), extracting information about networks object’s attributes may be difficult or even in many cases impossible.In these cases, predicting unknown attributes based on other objects attributes according to network structure can be extremely useful.Even more, finding a representative sample set of objects and trying to obtain their attributes in order to predict other object’s attributes with this obtained data can be an interesting problem. Finding such a set of objects with minimum size while giving maximizing accuracy in predicting other object’s... 

In this research, we want to find a point of the kernel in an unknown star-shaped polygon by a robot with minimal sensing, such that the path is not far from the optimum path. The robot has a gap sensor which detects the dicontinuities (gaps) in its visibility polygon and detects the direction of gaps. The robat can move toward or against these gaps. Also, the robot has a compass, and detects the North, the West, the South and the East. The robot detects the position of gaps between these directions, and also, can move along these directions. In this research, we present an on-line algorithm, by which this robot can find a point of the kernel in an unknown star-shaped polygon. The... 

Planar visibility computing is defned as determining the region of the plane that is visible from a specifc observer. This concept has many applications in computer graphics, robotic and computer games. In certain visibility problems, counting the number of visible objects in an appropriate time is required. For obtaining a solution fast, current algorithms give an approximated count. In this thesis, we consider visibility testing problem and visibility counting problem.For a given set S = fs1; s2; :::; sng of non-intersecting segments and a query point p in the plane, the visibility testing problem checks the inter-visibility of p and a segment si 2 S and the visibility counting problem... 

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... 

Nowadays, we observe the growth in the number of mobile smart phones. These smart phones have had an impressive progress in software and hardware. Many studies have focused on utilizing this new platform. One of these areas of research is collecting information from environment.Two major challenges for a successful crowdsourcing system are engaging a sufficient number of workers and validating of their registered data, which make the system more reliable. Collecting data from different points of a territory can be defined as some tasks and should be assigned to users near those tasks properly. Some users want a monetary reward for the cost they incur. On the other hand, information... 

In this study, we consider the fair division problem. In this problem, a heterogeneous resource must be fairly divided among a set of agents with different preferences.The resource can be either a divisible good (i.e., time, land), or a set of indivisible goods. When the resource is a single divisible good, the problem is commonly known as cake cutting. To measure fairness, several notions are defined, i.e., envy-freeness, proportionality, equability, maximin-share. In this thesis, we first give a formal definition of these notions. Next, we present our results for envy-freeness and maximin-share.First, we prove the existence of an allocation that guarantees each agent a factor 3/4 of his... 

In this research, we focus on r-gather and (r; ϵ)-gather clustering. In the r-gather clustering, the input points are in metric space and must be clustered such that each cluster has at least r points and the objective is to minimize the radius of clustering. (r; ϵ)-gather clustering is a kind of r-gather clustering such that at most nϵ points can be unclustered. MapReduce model is one of the most used parallel models to process huge data and processes the input data in some machine simultaneously in parallel.In this research, we give a lower bound for the approximation factor of r-gather clustering in MapReduce model. This lower bound works in MapReduce model even an optimal algorithm... 

The standard model of Cosmology (ΛCDM, based on the cosmological constant and cold dark matter) is the simplest model that many of its predictions match with observations. Large scale observations are one of the most important observational data in Cosmology. This type of observation reveals that the cosmos have a web-like structure at large scales called "Cosmic web". This web consists of dense regions full of galaxies (Knot), long filamentary structures (Filament), flat sheets (Sheet), and low-density vast regions (Void). The cosmic web is the most prominent representative of the distribution of galaxies and dark matter in large scales and studying it can provide cosmologists with valuable... 

In Spatial Voting Theory, distortion is a measure of how good the winner is. It is proved that no deterministic voting mechanism can guarantee a distortion better than 3, even for simple metrics such as a line. In this study, we wish to answer the following question: how does the distortion value change if we allow less motivated agents to abstain from the election? We consider an election with two candidates and suggest an abstention model, which is a more general form of the abstention model proposed by Kirchgassner. We define the concepts of the expected winner and the expected distortion to evaluate the distortion of an election in our model. Our results fully characterize the distortion... 

This document deals with the following results in details:Given a simple polygon P with $n$ vertices, the visibility polygon (VP) of a point q, or a segment pq inside P can be computed in linear time. It is known that the visibility polygon of a point inside a polygon in the presence of a mirror can be computed in linear time. We propose a linear time algorithm to extend the VP of a viewer (point or segment) by converting some edges of P into mirrors (reflecting-edges with specular type of reflection), such that a given non-visible segment uw can also be seen from the viewer.Various definitions for the visibility of a segment, such as weak, strong, or complete visibility, are considered. Our... 

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,... 

Many geometric problems have algorithms that exist on paper for them, such as the Convex Hull problem [1], Minimum Spanning Tree [2], Voronoi Diagram [3], Closest Pair of Points [4], Largest Empty Circle [5], Smallest Enclosing Circle [6], and more. In all of these problems, the assumption is that a certain number of points are given as input, and we must perform various operations on these points based on the nature of the problem. Furthermore, a stronger assumption is that these points are given to us precisely, but in reality, this is not the case, and for various reasons, it is not possible to determine the exact locations of these points. Therefore, it can be said that we are dealing...