Sharif Digital Repository

Designing a rapid transit network which is capable of providing a convenient coverage for passengers is studied in thisdoctoral thesis. First, a mathematical model of rapid transit network design which is a mixed integer program is presented (C_RTND). Objective function of the model is maximization of acceptable transit coverage and the model is capable of considering different rapid transit technologies. Furthermore, for each technology capacity constraint is considered in the model. Second, a heuristic algorithm is developed and used to solve the proposed model. The algorithm consists of 3 main parts: candidate line generation, network evaluation and a search algorithm for selecting a good... 

Problem of 2-colorability of hypergraphs was introduced by Erd?os in 1963, and there are many results about this problem until now. In this thesis we consider this problem from the algorithmic viewpoint. In all of the algorithms we assume that the given hypergraph is 2-colorable and we want to color it. By using a simple construction, it was shown that for every r = 3, the problem of coloring of hypergraphs is as hard as the problem of coloring graphs. If NP ?= ZPP12, it is impossible to approximate the chromatic number of r-uniform hyhpergraphs with n vertices by a factor of n1-? for any fixed ? > 0, in time polynomial of n. In reference [KS03] a coloring algorithm with approximation factor... 

In this research, we consider the question of finding approximate bounds on some of computational geometry problems with uncertain data. We use color spanning set to model the uncertainty. Given a set of n points colored with m colors in d-dimension. The problem of minimum diameter in color spanning set model is finding a set of m points with distinct colors so as to minimize diameter of the points. We give an algorithm with an approximation factor (1 + ϵ) with running time O(21ϵd .ϵ−2d.n3) which improves the previous results. Next,we consider a new problem of finding bounds on unit covering in color-spanning set model:Minimum color spanning-set ball covering problem is to select m points of... 

A social network is a social structure made up of individuals (or organizations) called ”nodes”, which are tied by one or more specific types of interdependency. These networks are new forms of distributed larg media which actually plays a critical role in distributing information and news among the people. because of the size and autonomos aspect of these kind od medias, taking control of them seems impossible. with the best hope we could think of some ways to detect information cascades through network.for example we could select a set of nodes as sensor inorder to detect information cascades as effectively as possible. in this thesis we studied cascade detection problem in scenario based... 

The Steiner forest problem is one of the most fundamental issues in network design that emerges in various contexts, such as the design of communication networks,transportation networks, VLSI circuits and phylogenetic network reconstruction. In this problem, we are given a connected weighted undirected graph and a special subset of vertices that are partitioned in pairs. The goal is to fnd a minimum-cost sub-graph in which each special vertex is connected to its mate. In this thesis we review a set of selected solutions for this problem and a few other related problems.For example, we study modeling and solving the s-t shortest path problem in order to gain insight into current Steiner... 

Due to recent advancements and wide usage of location detection devices, huge amount of data are collected by GPS and cellular technologies which exhibits moving objects trajectories. Using this information, it is possible to track a set of objects over a long period of time, as happens for instance in studying animal migration. Always, in these situations it is undesirable or even impossible (due to process and storage limits) to store the complete stream of positioning data. Then, simplifying a trajectory as a data reduction technique is the option for resolving such problems. Moreover, there is an increasing interest in queries capturing ”aggregate” behavior of trajectories as groups like... 

In examining protein-protein interaction networks, we often encounter similar and repetitive schemes. Examination of these designs, which often appear in the form of motifs and similar patterns, reveals important information such as the type of protein linkage and many of the internal similarities between these networks. The ability to recognize these similarities plays an important role in identifying the function of genes, recognizing the relationships between diseases, and making drugs. We know that exact algorithms for examining subgraph isomorphism are np-hard and time-consuming and infeasible in large networks; Therefore, in practice, approximate and heuristic algorithms are used and... 

Cake Cutting is an old problem that studies how to allocate a resource among a number of agents to achieve fairness or maximize the revenue by selling the chunks fairly. The primary assumption in the conventional methods of studying Cake Cutting was that the allocator knows everything about the agents and their valuation functions for the different cuts of the cake, which could be impossible in real life. Here we addressed a new setting for an online Cake Cutting problem with unconnected pieces and studied four different objectives upon the setting. There we studied fair and efficient Online Cake Cutting by means of linear fairness and envy freeness. We also added a payment rule to study the... 

In this thesis, we study the heterogeneous vehicles routing problem, which is a general-ization of the well-known travelling salesperson problem. In this problem, we are given a set of heterogeneous vehicles located in specific depots, along with a set of customers in the form of a graph. The vertices of the graph represent clients and depots, and the weight of edges represents the cost of travel between vertices of the graph. The goal is to find a subgraph for each vehicle so that the union of the subgraphs contain all customers and the total travel cost is minimized. The heterogeneity here means that the cost of traversing edges for each vehicle might be different. In this work, we briefly... 

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... 

With the emergence of massive datasets, storing all of the data in memory is not feasible for many problems. This fact motivated the introduction of new data processing models such as the streaming model. In this model, data points arrive one by one and the available memory is too small to store all of the data points. For many problems, more recent data points are more important than the old ones. The sliding window model captures this fact by trying to find the solution for the n most recent data points using only o(n) memory. The k-center problem is an important optimization problem in which given a graph, we are interested in labeling k vertices of the graph as centers such that the... 

Given a graph G with a set of terminals, two weight functions c and d defined on the edge set of G, and a bound D, a popular NP-hard problem in designing networks is to find the minimum cost Steiner tree (under function c) in G, to connect all terminals in such a way that its diameter (under function d) is bounded by D. Marathe et al. [1] proposed an (O(log2n);O(log2n)) approximation algorithm for this bicriteria problem, where n is the number of terminals. The first factor reflects the approximation ratio on the diameter bound D, and the second factor indicates the cost-approximation ratio. Later, Kapoor and Sarwat [2] introduced a parameterized approximation algorithm with performance... 

This thesis introduces and investigates a new kind of scheduling model, in which the total amount of computational resources to be allocated at each moment by the processor is constrained and upper bounded by a constant. The time for a task to be executed is also dependent on the computational resources, dedicated to it by the processor, assuming that the multiplication of the execution time by the dedicated computational resources is a constant for each job. We investigate various objective functions, such as minimizing the number of tardy jobs, minimizing maximum latency and etc, under varying constraints. The investigated objective functions are: a) Minimize number of tardy jobs b)... 

We study the problem of preclustering a set B of imprecise points in Rd. we wish to cluster the regions specifying the potential locations of the points such that, no matter where the points are located within their regions, the resulting clustering approximates the optimal clustering for those locations. We consider k-median clustering, and obtain the following results.First we present a (6k, 2)-preclustering in R2. Then we present a preclusterings for balls in Rd, including a (3k, α)-preclustering with α = 13.9 for the k-median problem. At last we show that we need at least 3k − 3 preclusters to obtain a bounded approximation ratio for this problem  

Network Function Virtualization (NFV) is a new paradigm for designing modern computer networks and data centers. NFV leverages the IT virtualization technologies to virtualize entire classes of network node functions into building blocks that may connect, or chain together to create communication services. In this research, we analysed and designed two offline and online algorithms for the problem of join optimization over placement and routing of network function chains in data centers. In the offline case, we showed that traditional randomized rouding works well and by help of chrnoff bound, we derive a new bound on performance gap. The online algorithm in both performance and resource... 

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... 

Graph partitioning and clustering are among the most important problems in computer science and engineering with a wide range of applications, to which a large number of research projects have attended. The normalized cut ratio is one of the best metrics for graph partitioning, giving rise to the ``Isoperimetry'' problem, which is, however, a challenging problem in its various forms. In this dissertation, we investigate the Isoperimetry problem. %, focusing on the Mean version. We prove that the Mean Isoperimetry problem on edge-weighted trees is solvable in strongly polynomial time. The algorithm can accomodate a wide range of constraints on the problem in the connected regime, including... 

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... 

Edit distance or Levenshtein distance is one of the most fundamental problems in computer science and engineering to measure the dissimilarity between strings.This problem is solvable in O(n^2) time using dynamic programming and in 2015 it was conditionally proven that no truly subquadratic time algorithm (\textit{i.e.}, O(n^{2-ε})) exists for edit distance.Since 2001, approximating edit distance within a constant factor was recognized as one of the biggest unsolved problems in the field of combinatorial pattern matching.This thesis designs seven approximation algorithms for edit distance and its related problems.Firstly, two quantum approximation algorithms are designed with constant... 

In this researh, we study the problem of profit maximization using viral marketing in social networks. In our model, the individual’s ultility value consists of two parts: a private utility and a value obtained by effects of other network members. Each member selects the service that maximizes its utility and Server can exhibit services in different qualities. First we focus on the problem from the Game Theory viewpoint and discuss on the existence and optimality of equilibrium. Next, we show that finding the best equilibrium is NP-hard. For the case of two services, we show that while P ̸= NP, no approximation algorithm with factor better than 2 exists for this problem. Finally, we try to...