Sharif Digital Repository

This paper presents the SkipTree, a new balanced, distributed data structure for storing data with multidimensional keys in a peer-to-peer network. The SkipTree supports range queries as well as single point queries which are routed in O(log n) hops. SkipTree is fully decentralized with each node being connected to O(logn) other nodes. The memory usage for maintaining the links at each node is O(log n log log n) on average and O(log2 n) in the worst case. Load balance is also guaranteed to be within a constant factor. © Springer-Verlag Berlin Heidelberg 2005  

In Spatial Voting Theory, distortion is a measure of how good the winner is. It has been 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 general form of the abstention model proposed by Kirchgässner. Our results characterize the distortion value and provide a rather complete picture of the model. ©2021 AI Access Foundation  

In this paper, we present a new and fast algorithm for generating the seeds set for web crawlers. A typical crawler normally starts from a fixed set like DMOZ links, and then continues crawling from URLs found in these web pages. Crawlers are supposed to download more good pages in less iterations. Crawled pages are good if they have high PageRanks and are from different communities. In this paper, we present a new algorithm with O(n) running time for generating crawler's seeds set based on HITS algorithm. A crawler can download qualified web pages, from different communities, starting from generated seeds set using our algorithm in less iteration  

In this paper, the elastic properties of monomeric actin (G-actin) and the trimer nucleus (G-actin trimer) in different states of nucleotide binding are estimated using steered molecular dynamic (SMD) simulations. Three nucleotide binding states are considered: ADP- and ATP-bound actin and nucleotide-free actin assemblies. Our results show that nucleotide binding and the corresponding changes in structure have significant effects on the mechanical behaviors of actin assemblies. Simulations reveal that the deformation behavior of G-actin monomers is generally elastic up to engineering strains of 16 and 40% in the tension and shear tests, respectively. In addition, the G-actin trimers react... 

Assume that we are given a set of points some of which are black and the rest are white. The goal is to find a set of convex polygons with maximum total area that cover all white points and exclude all black points. We study the problem on three different settings (based on overlapping between different convex polygons): (1) In case convex polygons are permitted to have common area, we present a polynomial algorithm. (2) In case convex polygons are not allowed to have common area but are allowed to have common vertices, we prove the NP-hardness of the problem and propose an algorithm whose output is at least (Formula presented.). (3) Finally, in case convex polygons are not allowed to have... 

We study two well-known planar visibility problems, namely visibility testing and visibility counting, in a model where there is uncertainty about the input data. The standard versions of these problems are defined as follows: we are given a set S of n segments in R 2 , and we would like to preprocess S so that we can quickly answer queries of the form: is the given query segment s∈S visible from the given query point q∈R 2 (for visibility testing) and how many segments in S are visible from the given query point q∈R 2 (for visibility counting). In our model of uncertainty, each segment may or may not exist, and if it does, it is located in one of finitely many possible locations, given by a... 

In this paper, we consider path simplification problem under difference area (diff-area) measure. Diff-area measure is defined as AA(Q) AB(Q) , where AA(Q) is the area under Q and above P and AB(Q) is the area above Q and under P (sec Figure 1). Bose et al. [1] presented an approximation algorithm for finding a simplificd path with at most k verticcs that minimizes the cliff-area measure which only works on i-monotone paths. The constraint of being i-monotone is restrictive in some applications like tracking bird migration paths or map boundary simplification. Here, we extend the method of Rosc et al. [1] and present algorithms with the same time complexities as theirs for gcneral paths.... 

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a continuous region ({Imprecise} model) or a finite set of points ({Indecisive} model). Given a set of inexact points in one of {Imprecise} or {Indecisive} models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on {Indecisive} model. We present an (formula presented) time approximation algorithm of factor (1+epsilon) for finding minimum diameter of a set of points in d dimensions. This improves the previously proposed algorithms for this... 

A geometric spanner on a point set is a sparse graph that approximates the Euclidean distances between all pairs of points in the point set. Here, we intend to construct a geometric spanner for a massive point set, using a distributed algorithm on parallel machines. In particular, we use the MapReduce model of computation to construct spanners in several rounds with inter-communications in between. An algorithm in this model is called efficient if it uses a sublinear number of machines and runs in a polylogarithmic number of rounds. In this paper, we propose an efficient MapReduce algorithm for constructing a geometric spanner in a constant number of rounds, using linear amount of... 

One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that the share allocated to an agent may affect the utilities of other agents. In this paper, we conduct a study of fair allocation of indivisible goods with positive externalities. Inspired by the models in the context of network diffusion, we present a simple and natural model, namely network externalities, to capture the externalities. To evaluate fairness in the network externalities model, we generalize the idea behind the notion of maximin-share (MMS) to achieve a new criterion, namely, extended-maximin-share (EMMS).... 

The number of known proteins is increasing every day; tens of thousands have been studied and categorized by now. In this chapter, we propose amodel for protein matching or extracting similar parts of two given proteins. We focus on the computational geometric approach and the graph matching method that are used to model and compare the sequence and 3D structure of proteins. The remainder ofthis chapter is organized as follows. We first have a glance at the related works. There are two major methods used in the literature: Delaunay tetrahedralization and similarity flooding.We explain the required information in the next section as background knowledge, and then propose a new idea in Sect.... 

Proteins are the main players in the game of life. Good understanding of their structures, functions, and behaviors leads to good understanding of drugs, diseases, and thus our health. So, much effort has been done to study and categorize proteins. Nowadays, tens of thousands of proteins have been found. Moreover, the problem of comparing the proteins is hard. Therefore efficient methods are needed to deal with this problem. In this paper, we used one important computational geometric method and one graph matching method: "Delaunay Tetrahedral-ization" and "Similarity Flooding" to propose a new idea to extract similar parts of proteins by combining both of these methods  

Given an undirected graph with weights associated with its edges, the Steiner tree problem consists of finding a minimum weight subtree spanning a given subset of (terminal) nodes of the original graph. Minimum Spanning Tree Heuristic (MSTH) is a heuristic for solving the Steiner problem in graphs. In this paper we first review existing algorithms for solving the Steiner problem in graphs. We then introduce a new parallel version of MSTH on three dimensional mesh of trees architecture. We describe our algorithm and analyze its time complexity. The time complexity analysis shows that the algorithm's running time is O(lg2 n) which is comparable with other existing parallel solutions. © 2007... 

The k-level Uncapacitated Facility Location (UFL) problem is a generalization of the UFL and the k-median problems. A significant shortcoming of the classical UFL problem is that often a few very distant customers, known as outliers, can leave an undesirable effect on the final solution. This deficiency is considered in a new variant called UFL with outliers, in which, in contrast to the other problems that need all of the customers to be serviced, there is no need to service the entire set of customers. UFL with Penalties (UFLWP) is a variant of the UFL with outliers problem in which we will decide on whether to provide service for each customer and pay the connection cost, or to reject it... 

One of the important yet insufficiently studied subjects in fair allocation is the externality effect among agents. For a resource allocation problem, externalities imply that the share allocated to an agent may affect the utilities of other agents. In this paper, we conduct a study of fair allocation of indivisible goods with positive externalities. Inspired by the models in the context of network diffusion, we present a simple and natural model, namely network externalities, to capture the externalities. To evaluate fairness in the network externalities model, we generalize the idea behind the notion of maximin-share (MMS) to achieve a new criterion, namely, extended-maximin-share (EMMS).... 

We introduce the notion of two-valued digit (twit) as a binary variable that can assume one of two different integer values. Posibits, or simply bits, in {0, 1} and negabits in {-1, 0}, commonly used in two's-complement representations and (n, p) encoding of binary signed digits, are special cases of twits. A weighted bit-set (WBS) encoding, which generalizes the two's-complement encoding by allowing one or more posibits and/or negabits in each radix-2 position, has been shown to unify many efficient implementations of redundant number systems. A collection of equally weighted twits, including ones with non-contiguous values (e.g., {-1, 1} or {0, 2}), can lead to wider representation range... 

We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of m nodes on the plane, the aim is to achieve some specific property by minimum movement of the nodes. We consider two specific properties, namely the connectivity (Con) and realization of a given topology (Topol). By minimum movement, we mean either the sum of all movements (Sum) or the maximum movement (Max). We obtain several approximation algorithms and some hardness results for these four problems. We obtain an O(m) -factor approximation for ConMax and ConSum and extend some known result on graphical grounds and obtain inapproximability results on the geometrical grounds. For the... 

Assume that we are given a set of points some of which are black and the rest are white. The goal is to find a set of convex polygons with maximum total area that cover all white points and exclude all black points. We study the problem on three different settings (based on overlapping between different convex polygons): (1) In case convex polygons are permitted to have common area, we present a polynomial algorithm. (2) In case convex polygons are not allowed to have common area but are allowed to have common vertices, we prove the NP-hardness of the problem and propose an algorithm whose output is at least (OPTlog(2n/OPT)+2log(n))1/4. (3) Finally, in case convex polygons are not allowed to... 

Polar Diagram [4] is a new locus approach for problems processing angles. The solution to many important problems in Computational Geometry requires some kind of angle processing of the data input. Using the Polar Diagrma as preprocessing, exhaustive searches to find those sites with smallest angle become unnecessary. In this paper, we use the notion of kinetic data structure [1][2] to model the dynamic case of polar diagram, i.e we maintain the polar diagram of a set of continuously moving objects in the scene. We show that our proposed structure meets the main criteria of a good KDS. © 2008 Springer-Verlag  

We study a classical problem in communication and wireless networks called Finding White Space Regions. In this problem, we are given a set of antennas (points) some of which are noisy (black) and the rest are working fine (white). The goal is to find a set of convex hulls with maximum total area that cover all white points and exclude all black points. In other words, these convex hulls make it safe for white antennas to communicate with each other without any interference with black antennas. We study the problem on three different settings (based on overlapping between different convex hulls) and find hardness results and good approximation algorithms