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Conditional Geometric Touringand Connectivity
, Ph.D. Dissertation Sharif University of Technology ; Zarei, Alireza (Supervisor)
Abstract
Finding optimize tours on a given sequence of objects has applications in robitic. A tour on a given sequence of objects is a path that touchs or cuts each of them, in order. In STOC′03 it is shown that finding such a shortest path for a sequence of convex polygons is polynomial solvable and it is NP-hard for non-convex polygons with intersections. The complexity of the problem for disjoint polygons is asked as the importest open peoblem. In 2008 an approximation algorithm is presented for this problem. We show that the problem is NP-hard in each Lp norm, even if each polygon consists of two unit line segments. Also, in 2003 the problem, with obstacles has been proposed as a future work. An...
Clustering and Embedding Graphs into Trees
, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
In this thesis, we study the following question stating that “how well a tree structure can approximate the clustering structure of a graph”.To do this, we first focus on the DJS algorithm proposed by Daneshgar et.al. and second we consider the minimum distortion tree approximation algorithm proposed by Abraham et.al.We conclude, using some experimental results, that the minimum spanning tree algorithm extracts some geometric aspects of the data set that the Abraham et.al. algorithm can not track
Computing Shortest path and Minimum Spanning Tree under Uncertainty
, M.Sc. Thesis Sharif University of Technology ; Zarei, Alireza (Supervisor)
Abstract
Computing shortest paths and minimum spanning trees are basic and well-known problems in computer science and graph theory; also they have been considered as basic subroutines for many practical algorithms. There exists optimal algorithms for solving these problems when information about the basic graph is certain and specified. But, in real applications when the graph is obtained by using measurement tools which have limited computing precision, practically we are facing a graph in which locations of vertices or weights of edges are estimated.In such cases determining upper bounds or lower bounds for solutions of the shortest path and the minimum spanning tree are estimations of the...
Minimum Color-spanning Tree
, M.Sc. Thesis Sharif University of Technology ; Abam, Mohammad Ali (Supervisor)
Abstract
In the general case of minimum color-spanning tree which is one of the color-spanning set problems, given a weighted graph with n vertices of k different colors, the goal is to find a subtree of minimum weight such that vertices of this subtree include all the colors in the graph. In the planar case, the input is a complete graph with n colored vertices on the plane and the weight of each edge is the Euclidean distance between its corresponding vertices. In this thesis we consider the problem of minimum color-spanning tree. To this end, first we present various color-spanning set problems and some other related problems like Steiner tree and we study the previous work on these problems. Then...
Sensitivity Analysis and Optimization in Network Flows
, Ph.D. Dissertation Sharif University of Technology ; Eshghi, Kourosh (Supervisor)
Abstract
In today's life, we look at each other, seeing different networks, such as power networks, telecommunication networks, transportation networks (freeways, roads, streets), rail networks, air service networks, shipping networks, Logistics networks (networks of construction and distribution), computer networks, Internet networks (e-commerce, banking networks), airline reservation networks, social networks and so on. In all of these networks, an entity such as man, product, car, electricity, message, information, aircraft, etc. from one source into a destination is moved according to the network's purposes and objectives.This thesis analyzes the sensitivity analysis and optimization of...
Determinantal Processes
, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract
Determinantal processes are a special family of stochastic processes that arise in physics (fermions), random matrices (eigenvalues), and in combinatorics (random spanning trees and non-intersecting paths). These processes have repelling property (points close to each other are chosen with low probability). Because of this repelling property, determinantal processes are approporiat for modeling some physical quantities (e.g. the position of electrons). Their probabilistic structure is described by operators on complex vector spaces and their eigenvalues. Determinantal processes have interesting properties, e.g. number of points in a region is a sum of independent Bernoulli random variables....
Investigating Geometric Proximity Problems on Moving Points
, M.Sc. Thesis Sharif University of Technology ; Zarei, Alireza (Supervisor)
Abstract
An interesting theoretical and practical set of problems in computer science is concerned with the study of spatial relations among objects in a geometric space. Examples of such problems for a set of points P are finding the closest pair of the points P, partitioning space into regions such that all points of a region have minimum distance to the same point in P, and computing the Euclidean minimum spanning tree on P. Moreover, we need mechanisms to efficiently update these properties when the points P are allowed to move or may be inserted or deleted. This is to avoid re-computation of these properties from scratch. Here, we consider the Euclidean minimum spanning tree (EMST) of a set of...
Edge Disjoint Spanning Trees and Eigenvalues
, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
Abstract
The spectrum of a graph is related to many important combinatorial parameters. Let (G), ′(G) be the maximum number of edge-disjoint spanning trees and edge-connectivity of a graph G,respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of (G), we use eigenvalue interlacing for quotient matrix associated to graph to get the relationship between eigenvalues of a graph and bounds of (G) and ′(G). We also study the relationship between eigenvalues and bounds of (G) and ′(G) in a multigraph G. In the first chapter we prove eigenvalue interlacing and give several applications of it for obtaining bounds for characteristic numbers of...
Developing Control Strategies for Consensus and Coverage in Multi-Agent Systems
, M.Sc. Thesis Sharif University of Technology ; Sayyaadi, Hassan (Supervisor)
Abstract
Over the past few years there has been a rapidly growing interest in analysis, design and optimization of various types of collective behaviors in networked dynamic systems. Collective phenomena (such as flocking, schooling, rendezvous, synchronization, and agreement) have been studied in a diverse set of disciplines. In many applications involving multi-agent systems, groups of agents are required to agree on certain quantities of interest; in other words, it is important to develop information consensus protocols for networks of dynamic agents. There are many practical situations where it is desirable or even required to achieve stable convergence in finite-time domain. In this work, a...
Comparing and Improving the Minimum Spanning Tree Algorithms in MapReduce
, M.Sc. Thesis Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
In recent decades, we have faced the enormous growth of data and graph volumes. This requires modern ways of computation and storage systems and algorithms. MapReduce is a known way of processing Big Data in a Parallel and primarily Distributed setting. Theoretical models (e.g., Massively Parallel Computation) for Algorithms using this paradigm commonly evaluate the number of rounds and needed communication. We study the Minimum Spanning Tree (MST) as a fundamental graph problem. This problem in MapReduce is harder for sparse graphs. We introduce an algorithm that performs well comparing previous studies, especially for sparse graphs.We present an empirical study by implementing some...
Special classes of mathematical programming models with fuzzy random variables [electronic resource]
, Article Journal of Intelligent and Fuzzy Systems, Published In: IOS Press ; Volume 19, Number 2, 2008 ; Nematian, Javad ; Sharif University of Technology
Abstract
In this paper, we will discuss two special classes of mathematical programming models with fuzzy random variables. In the first model, a linear programming problem with fuzzy decision variables and fuzzy random coefficients is introduced. Then an algorithm is developed to solve the model based on fuzzy optimization method and fuzzy ranking method. In the second model, a fuzzy random quadratic spanning tree problem is presented. Then the proposed problem is formulated and solved by using the scalar expected value of fuzzy random variables. Furthermore, illustrative numerical examples are also given to clarify the methods discussed in this paper
Multispanning tree zone-ordered label-based routing algorithms for irregular networks
, Article IEEE Transactions on Parallel and Distributed Systems ; Vol. 22, issue. 5 , 2011 , p. 817-832 ; ISSN: 10459219 ; Moinzadeh, P ; Sarbazi-Azad, H ; Zomaya, A.Y ; Sharif University of Technology
Abstract
In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into...
Adaptive flocking control of nonlinear multi-agent systems with directed switching topologies and saturation constraints
, Article Journal of the Franklin Institute ; Volume 350, Issue 6 , August , 2013 , Pages 1545-1561 ; 00160032 (ISSN) ; Haeri, M ; Sharif University of Technology
2013
Abstract
In this paper, we propose and analyze flocking algorithms in a network of second-order agents with bounded control inputs and nonlinear intrinsic dynamics. We consider a general switching network topology, for velocity information exchange, rather than undirected or fixed directed network topology with a directed spanning tree. The proposed adaptive controller architecture applies a leader-following strategy in which the pinning scheme is defined based on the interaction topology. Finally, some examples are presented to illustrate the theoretical results
Optimal pipe diameter sizing in a tree-structured gas network: A case study
, Article International Journal of Industrial and Systems Engineering ; Volume 12, Issue 3 , 2012 , Pages 346-368 ; 17485037 (ISSN) ; Mahdavi, I ; Mahdavi Amiri, N ; Sharif University of Technology
2012
Abstract
We design an optimal pipe diameter sizing in a tree-structured natural gas network. Design of pipeline, facility and equipment systems are necessary tasks to configure an optimal natural gas network. A mixed-integer programming model is formulated to minimise the total cost in the network. The aim is to optimise pipe diameter sizes so that the location-allocation cost is minimised. Pipeline systems in natural gas network must be designed based on gas flow rate, length of pipe, gas maximum drop pressure allowance and gas maximum velocity allowance. We use information based on relationship among gas flow rates and pipe diameter sizes considering gas pressure and velocity restrictions. We apply...
Kinetic Euclidean minimum spanning tree in the plane
, Article Journal of Discrete Algorithms ; Volume 16 , October , 2012 , Pages 2-11 ; 15708667 (ISSN) ; Zarei, A ; Sharif University of Technology
Elsevier
2012
Abstract
This paper presents a kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of moving points in 2-dimensional space. For a set of n points moving in the plane we build a KDS of size O(n) in O(nlogn) preprocessing time by which the EMST is maintained efficiently during the motion. This is done by applying the required changes to the combinatorial structure of the EMST which is changed in discrete timestamps. We assume that the motion of the points, i.e. x and y coordinates of the points, are defined by algebraic functions of constant maximum degree. In terms of the KDS performance parameters, our KDS is responsive, local, and compact. The...
Kinetic pie delaunay graph and its applications
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7357 LNCS , 2012 , Pages 48-58 ; 03029743 (ISSN) ; 9783642311543 (ISBN) ; Rahmati, Z ; Zarei, A ; Sharif University of Technology
2012
Abstract
We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yao graph and Euclidean minimum spanning tree (EMST). We efficiently maintain the Pie Delaunay graph where the points are moving in the plane. We use the kinetic Pie Delaunay graph to create a kinetic data structure (KDS) for maintenance of the Yao graph and the EMST on a set of n moving points in 2-dimensional space. Assuming x and y coordinates of the points are defined by algebraic functions of at most degree s, the structure uses O(n) space, O(nlogn) preprocessing time, and processes O(n 2 λ 2s∈+∈2(n)β s + 2(n)) events for the Yao graph and O(n 2 λ 2s + 2(n)) events for the...
Optimization of tree-structured gas distribution network using ant colony optimization: A case study
, Article International Journal of Engineering, Transactions A: Basics ; Volume 25, Issue 2 , 2012 , Pages 141-158 ; 17281431 (ISSN) ; Mahdavi, I ; Mahdavi Amiri, N ; Tafazzoli, R ; Sharif University of Technology
Materials and Energy Research Center
2012
Abstract
An Ant Colony Optimization (ACO) algorithm is proposed for optimal tree-structured natural gas distribution network. Design of pipelines, facilities, and equipment systems are necessary tasks to configure an optimal natural gas network. A mixed integer programming model is formulated to minimize the total cost in the network. The aim is to optimize pipe diameter sizes so that the location-allocation cost is minimized. Pipeline systems in natural gas network must be designed based on gas flow rate, length of pipe, gas maximum pressure drop allowance, and gas maximum velocity allowance. We use the information regarding gas flow rates and pipe diameter sizes considering the gas pressure and...
Latency considerations in IEC 61850-enabled substation automation systems
, Article IEEE Power and Energy Society General Meeting, 24 July 2011 through 28 July 2011, Detroit, MI ; 2011 ; 19449925 (ISSN) ; 9781457710018 (ISBN) ; Mousavi, M. J ; Vakilian, M ; Sharif University of Technology
Abstract
Substation Automation Systems (SAS) offer powerful, fast, and viable ways to design, automate, and implement substation protection, control, and monitoring functions in modern transmission and distribution grids. Today's SAS -more than ever- rely on the adoption of IEC61850 as a worldwide standard for interoperability and dependable peer-to-peer and substation communications. Being based on the Ethernet computer networking technology, the reliability issues associated with latency in 61850-enabled SAS is of a design consideration. Unpredictability is the most important challenge for latency assessment. This paper discusses the background framework for latency evaluations in SAS by...
Kinetic Euclidean minimum spanning tree in the plane
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 7056 LNCS , 2011 , Pages 261-274 ; 03029743 (ISSN) ; 9783642250101 (ISBN) ; Zarei, A ; Sharif University of Technololgy
2011
Abstract
This paper presents the first kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of n moving points in 2-dimensional space. We build a KDS of size O(n) in O(nlogn) preprocessing time by which their EMST is maintained efficiently during the motion. In terms of the KDS performance parameters, our KDS is responsive, local, and compact
Multispanning tree zone-ordered label-based routing algorithms for irregular networks
, Article IEEE Transactions on Parallel and Distributed Systems ; Volume 22, Issue 5 , July , 2011 , Pages 817-832 ; 10459219 (ISSN) ; Moinzadeh, P ; Sarbazi Azad, H ; Zomaya, A. Y ; Sharif University of Technology
Abstract
In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into...