Sharif Digital Repository

Approximate Agreement (AA) is one of the most important issues in distributed networks in which non-faulty processes execute a voting algorithm to reach the values that are very close to each other. AA for Partially Connected Networks (PCNs) is very limited because a node may not have a complete view of the whole network which makes it difficult to reach the convergence. This research proposes a convergent Fuzzy algorithm for synchronous distributed networks in the presence of faulty or Byzantine processes. When each node receives a new value from its neighbors,it runs the convergent Fuzzy algorithm. If the received value is not in the expected range of values, the processor can discard the... 

We study a class of optimization network problems on pairs of structures. In particular, given n pairs of points P = f(p1; q1); (p2; q2); : : : ; (pn; qn)g, in the plane or in general metric space, the goal is to color points of each pair, one red and the other blue, so as a given cost function on the red points and blue points is optimized. The cost functions studied previously are MST, TSP, and matching. In this work, we consider a new cost function; i.e., the diameter of each colored point set, and present efficient algorithms to solve the problem according to some objective functions  

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... 

Since the amount of data is increasing, it is important to reduce the size of components and circuits. For instance, bus routing problem, rectangle scape problem, and minimizing number of layers are important problems in printed circuit boards. Rectangle scape problem can be used as an estimation for minimizing number of layers problem. To minimize number of layers in this problem, we are given some axis-parallel rectangles inside a axis-parallel rectangular region. The objective is to extend one of the four boundaries of each rectangle in a certain direction such that all rectangles can be placed without any conflict in minimum number of layers. In this thesis, we analyze a common greedy... 

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... 

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,... 

The edge coloring problem is one of the most fundamental problems in graph theory. In this problem, the task is to assign colors to edges so that no two incident edges have the same color. Although finding an optimal edge coloring is NP-hard, Vizing’s theorem asserts that ∆+1 colors are always sufficient, denoting the maximum degree in the graph by ∆.Due to significant increase in the volume of data, for most problems, storing the whole data is not possible. This had led to emergence of new models of processing data such as data streaming model. In semi-streaming model the input graph is represented as a stream of edges, and the storage space of an algorithm is bounded by O(n. polylog n). So... 

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... 

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... 

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  

Power dominating set is a concept in graph theory that was first defined as a result of studying the controllability of electric power systems. Assume that a graph G and a subset S of vertices of G are given. First, we color all vertices in S black, and all other vertices of G white. Then we color all vertices that have a neighbor in S black (Domination step). After that, for each black vertex v, if all neighbors of v except one (the vertex u) are black, then we also color the vertex u black (Propagation step). If after a number of Propagation steps all vertices of G are black, then we call S a power dominating set of G. The minimum cardinality of a power dominating set of G is called the... 

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 consider the problem of finding longest paths in some special classes of graphs. This problem is NP-hard in general case. It has been proven that there is no constant factor polynomial time approximation algorithm for this problem, unless P = NP. Therefore, the problem is usually solved for special classes of graphs.In this research, we focus on finding longest paths in solid grids, and propose a factor 3/4 approximation algorithm. Our algorithm improves the best current result which has an approximation factor of 2/ 3 . As a side result, we also propose a linear time algorithm for finding Hamiltonian cycle in a subset of Hamiltonian solid grids which improves the... 

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 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... 

In this thesis, we focus on a subset of geometric optimization problems (including k-center) in the Sliding Window model. The sliding window model is driven from the Data Stream model in which input points arrive one by one and the space is limited. The main diffrenece of these two models is that in the sliding window model we are interested in the N latest points not all of the arrived points. In this thesis, we study Minimum Enclosing Ball, 2-center, and Euclidean k-center in the Sliding Window model. We provide a (1 + ")-approximation algorithm for MEB in d-dimensions. To our knowledge there is no algorithm for MEB in d-dimensions where d >2. We also provide a (1 + ")-approximation... 

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... 

Data clustering is simply the process of partitioning data in to non empty subsets, called clusters, such that in every clusters members are related due to an pre-defined objective function. Assume that there are n points in eulcidian d-dimensional space and the goal is to determine k points in space as a representive of each cluster so that in every cluster, members have the least value of an objective function which is related to their distances from representatives. From most important types of data clustering problem we may mention k-center, k-median and k-means problem in which the objective functions are respectively, minimizing the maximum, sum and sum of squares of distance of every... 

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... 

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...