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... 

This thesis presents a dynamic multidimensional data structure, which is called Improved Skip Quadtree for peer-to peer networks. This data structure is the Improved version of Skip Quadtree which originally presented jointly by D.Eppstein, M.T.Goodrich, and J.Z.Sun. It tries to combine the best features of two well-known data structures; hieracical structure search quadtree, and skip list. In this thesis, it is tried to focus on algorithms for inserting and deleting points in both skip quadtree and Improved skip quadtree, which is fast method for performing point location and approximate range queries. The result of experimentation and implementation of this structure shows that it can be... 

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... 

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,... 

The study of visibility is at least 100 years old, when in 1913 Brunn proved a theorem about the kernel of a set. By now, visibility has become one of the most studied notions in computational geometry. The reasons are two-fold: 1) such problems arise naturally in areas where computational geometry tools and algorithms _nd applications including: computer graphics, robotics, motion planning, geographic information systems, computer games, computer-aided architecture, and pattern recognition; and where 2) their solutions are required, or serve as building blocks in the development of solutions to other problems, such as shortest paths or motion planning problems. Many natural problem... 

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... 

Visibility is an important topic in computational geometry, computer graphics, and motion planning. Two points inside a polygon are visible to each other if their connecting segment remains completely inside the polygon. Visibility polygon of a point in a simple polygon P is the set of points inside P that are visible from the point. The visibility problem has also been considered for line segments. A point v is said to be weakly visible to a line segment pq if there exists a point w 2 pq, such that w and v are visible to each other. The problem of computing the weak visibility polygon (or WVP) of pq inside a polygon P is to compute all points of P that are weakly visible from pq. In this... 

This thesis examines cooperating robots with minimal sensing to find the particular target described in unknown surroundings. Due to the very high cost sensor robots, Recently researchers are going to use of simple sensors for robot in special purpose and reduce costs. Of course it is clear that doing so will decrease the accuracy and efficiency of the robot and we are going to provide an efficient algorithm for performing the desired action with a good competitive factor. In this thesis the robots movement is online and robots have no knowledge of their environment (such as maps), they only using the data is gathered from the sensors to decide how to move. The accuracy of this information... 

Shortest path computation is one the fundamental problems in computer science. Triangulated Irregular Networks (TINs) are used in computational geometry to represent terrians and geometric surfaces. One of the most efficient mothods to solve the shortest path problem on a TIN is reducing it to shortest path problem on a graph. This reduction from continuous space to discrete space results in approximate solutions, but acceptable in real applications. In real applications we still encounter a large graph and using the simple Dijkstra algorithm consumes a lot of times. Memory shortage is another issue. Parallel processing could be a solution in this case. Multicore industry caused a... 

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... 

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... 

In this thesis, we present different algorithms for path simplification. We first study this problem under area measures. We present an approximation algorithm for sum-area measure and an optimal algorithm for diff-area measure. Both of these algorithms can be applied on general paths. Moreover, we study the homotopic path simplification. We present a general framework for path simplification which work for desired error measure. We first present a strongly homotopic simplification algorithm for x-monotone paths. Also, we study the strongly homotopic simplification for general paths. We present a geometric tree data structure and present an algorithm based on this data structure.... 

The concept of Online-Distributed Mechanism Design, is taken from the two concepts of Online Mechanism and Distributed Mechanism and speaks of an environment which is dynamic when there is no trusted center to do the computation. This problem is stated in this thesis for the first time and by the thesis we gave the first results in some of the up coming fields of Online-Distributed Mechanism. These feilds would be defined by different assupmtions about dynamic environments and the way of distributing of computation among agents. We consider single valued preference domains in the absence of any trusted center and in the presence of an enforcer. Then we try to design truthful auctions for... 

The visibility is one of the most important problems in computational geometry. Two points are said to be visible to each other, if the line segment that joins them does not intersect any obstacles. The art gallery problem is a well-studied visibility problem in computational geometry. It originates from a real-world problem of guarding an art gallery with the minimum number of guards who together can observe the whole gallery. In many of applications, the “guards” are “landmarks” deployed in an environment to help provide navigation and localization service to mobile robots. The mobile device communicates with these landmarks through wireless, or other “line-of-sight” signaling... 

TIN (Triangulated Irregular Network) is a Data Structure for storing and manipulating surfaces like maps in GIS applications or 3D models in game engines or Vector Fields . A TIN contains a set of triangulated vertices (which has irregular distribution) and each vertex shows a point in space . We trying to find the smallest possible set (optimal solution) of vertices from input surface (which given as a TIN) to approximate input surface with epsilon error which is given as input. also, surface simplification problem is a member of NP-Hard class. The hardness of problem makes it infeasible to find an optimal solution in polynomial time. So we try finding an approximate algorithm for this... 

Evaluating the enviroment for achieving efcient kwnoledge in order to justifed environment recognition and making decision based on data analysis is proponed in many felds.One of these problems is Visibility Problem. The Recieved data from real world as input, for visibility problem, is uncertain such that the recieving data of two different measurments will be different with high probability. Therefore, we defne the goal of this research to solving the visibility problem conditioned to that objects or segments are uncertain.Consider ”S” as a set of ”n” uncertain segments in plane. Each uncertain segment locates in two certain places and with probability 1 2 in each place, the goal is to... 

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... 

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... 

Given a set of obstacles as an arrangement of geometric shapes in the plane, we would like to find a path from the initial point s to the target point t that crosses the minimum number of obstacles. In other words, the goal is to determine the minimum number of obstacles that need to be removed to exist a collision-free path between s and t.On one hand, this problem can be used for measuring the strength of barrier coverage which is a fundamental concept in wireless sensor networks (WSNs), and on the other hand, it has been considered as a robot motion-planning problem. The objective of barrier coverage is to guarantee that any path from the start point to the target point, will intersect at...