Sharif Digital Repository

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility, weak and complete segment visibility, and the construction of the visibility graph. We also investigate the natural query versions of these problems, when α is either fixed or specified at query time  

Given a metric graph G, we are concerned with finding a spanning tree of G where the maximum weighted degree of its vertices is minimum. In a metric graph (or its spanning tree), the weighted degree of a vertex is defined as the sum of the weights of its incident edges. In this paper, we propose a 4.5-approximation algorithm for this problem. We also prove it is NP-hard to approximate this problem within a 2 - ε factor. © 2007 Elsevier B.V. All rights reserved  

When our sources are graph signals, a more efficient algorithm for Blind Source Separation (BSS) can be provided by using structural graph information along with statistical independence and/or non-Gaussianity. To the best of our knowledge, the GraphJADE and GraDe algorithms are the only BSS methods addressing this issue in the case of known underlying graphs. However, in many real-world applications, these graphs are not necessarily a priori known. In this paper, we propose a method called GraphJADE-GL (GraphJADE with Graph Learning) that jointly separates the graph signal sources and learns the graphs related to them accurately, in an alternating style. © 1994-2012 IEEE  

When a loan is approved for a person or company, the bank is subject to credit risk; the risk that the lender defaults. To mitigate this risk, a bank will require some form of security, which will be collected if the lender defaults. Accounts can be secured by several securities and a security can be used for several accounts. The goal is to fractionally assign the securities to the accounts so as to balance the risk. This situation can be modeled by a bipartite graph. We have a set S of securities and a set A of accounts. Each security has a value vi and each account has an exposure ej. If a security i can be used to secure an account j, we have an edge from i to j. Let fij be the part of... 

Visibility graph of a simple polygon is a graph with the same vertex set in which there is an edge between a pair of vertices if and only if the segment through them lies completely inside the polygon. Each pair of adjacent vertices on the boundary of the polygon are assumed to be visible. Therefore, the visibility graph of each polygon always contains its boundary edges. This implies that we have always a Hamiltonian cycle in a visibility graph which determines the order of vertices on the boundary of the corresponding polygon. In this paper, we propose a polynomial time algorithm for determining such a Hamiltonian cycle for a pseudo-triangle polygon from its visibility graph. © 2020, IFIP... 

In this paper, we first introduce a network of learning automata, which we call it as distributed learning automata and then propose some iterative algorithms for solving stochastic shortest path problem. These algorithms use distributed learning automata to find a policy that determines a path from a source node to a destination node with minimal expected cost (length). In these algorithms, at each stage distributed learning automata determines which edges to be sampled. This sampling method may result in decreasing unnecessary samples and hence decreasing the running time of algorithms. It is shown that the shortest path is found with a probability as close as to unity by proper choice of... 

Graph signal processing (GSP) have found many applications in different domains. The underlying graph may not be available in all applications, and it should be learned from the data. There exist complicated data, where the graph changes over time. Hence, it is necessary to estimate the dynamic graph. In this paper, a new dynamic graph learning algorithm, called dynamic K-graphs, is proposed. This algorithm is capable of both estimating the time-varying graph and clustering the temporal graph signals. Numerical experiments demonstrate the high performance of this algorithm compared with other algorithms. © 2021 European Signal Processing Conference, EUSIPCO. All rights reserved  

Many theoretical studies have compared the hypercube and star graphs from a graph theoretical viewpoint, under structural and algorithmic properties. None of these studies have, however, considered real working conditions and implementation constraints. In this paper, the hypercube and star graphs are compared in view of fault tolerance and technological implementation constraints. In order to realize a fair comparison, we use the unsafely-vector fault tolerant routing algorithm, recently introduced in [1] and [2], for the hypercube and star graph. Under two implementation constraints, namely constant bisection bandwidth and constant node pin-out, we have compared the performance of the two... 

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... 

Today, public awareness about the benefits of using ontologies in information processing and the semantic web has increased. Since ontologies are useful in various applications, many large ontologies have been developed so far. But various areas like publication, maintenance, validation, processing, and security policies need further research. One way to better tackle these areas is to partition large ontologies into sub partitions. In this paper, we present a new method to partition large ontologies. For the proposed method, three steps are required: (1) transforming an ontology to a weighted graph, (2) partitioning the graph with an algorithm which recognizes the most important concepts,... 

Edit distance is one of the most fundamental problems in computer science. Tree edit distance is a natural generalization of edit distance to ordered rooted trees. Such a generalization extends the applications of edit distance to areas such as computational biology, structured data analysis (e.g., XML), image analysis, and compiler optimization. Perhaps the most notable application of tree edit distance is in the analysis of RNA molecules in computational biology where the secondary structure of RNA is typically represented as a rooted tree. The best-known solution for tree edit distance runs in cubic time. Recently, Bringmann et al. show that an O(n2.99) algorithm for weighted tree edit... 

In this paper, we present a randomized LOCAL constant approximation factor algorithm for minimum dominating set (MDS) problem and minimum total dominating set (MTDS) problem in graphs. The approximation factor of this algorithm for planar graphs with no 4-cycles is 18 and 9 for MDS and MTDS problems, respectively. © 2020 Owner/Author  

The anti-Ramsey numbers are a fundamental notion in graph theory, introduced in 1978, by Erdös, Simonovits and Sós. For given graphs G and H the anti-Ramsey number ar(G, H) is defined to be the maximum number k such that there exists an assignment of k colors to the edges of G in which every copy of H in G has at least two edges with the same color. Usually, combinatorists study extremal values of anti-Ramsey numbers for various classes of graphs. There are works on the computational complexity of the problem when H is a star. Along this line of research, we study the complexity of computing the anti-Ramsey number ar(G, Pk), where Pk is a path of length k. First, we observe that when k is... 

Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the... 

The surface area which is defined as the number of vertices at a given distance from a base vertex of a graph is considered to be as one of the most useful yet abstract combinatorial properties of a graph. The applicability of surface area spans many problem spaces such as those in parallel and distributed computing. These problems normally involve combinatorial analysis of underlying graph structures (e.g., spanning tree construction, minimum broadcast algorithms, efficient VLSI layout, performance modeling). In this paper, we focus on the problem of finding the surface area of a class of popular graphs, namely the family of WK-recursive and swapped networks. These are attractive networks... 

This paper studies an iterative stochastic algorithm for solving the stochastic shortest path problem. This algorithm, which uses a distributed learning automata, tries to find the shortest path by taking a sufficient number of samples from the edges of the graph. In this algorithm, which edges to be sampled are determined dynamically as the algorithm proceeds. At each iteration of this algorithm, a distributed learning automata used to determine which edges to be sampled. This sampling method, which uses distributed learning automata, reduces the number of samplings from those edges, which may not be along the shortest path, and resulting in a reduction in the number of the edges to be... 

Lift path planning is a significant subtask in constructability analysis, sequencing, and scheduling of congested industrial modular projects, impacting project cost, and safety. Although intuitive lift planning is still prevalent among the practitioners, this manual process might be tedious and error-prone for hundreds of lifts. This research presents an automated lift path planning method for heavy crawler cranes in no-walk scenarios employing a robotics approach. This method treats the lifted object as a three-degree-of-freedom convex mobile robot with discretized rotational and continuous translational motions. The proposed resolution-complete method models the crane capacity chart,... 

We propose a novel method for the clustering of point-cloud data that originate from single-molecule localization microscopy (SMLM). Our scheme has the ability to infer a hierarchical structure from the data. It takes a particular relevance when quantitatively analyzing the biological particles of interest at different scales. It assumes a prior neither on the shape of particles nor on the background noise. Our multiscale clustering pipeline is built upon graph theory. At each scale, we first construct a weighted graph that represents the SMLM data. Next, we find clusters using spectral clustering. We then use the output of this clustering algorithm to build the graph in the next scale; in... 

Given a social network modeled as a weighted graph GG, the influence maximization problem seeks kk vertices to become initially influenced, to maximize the expected number of influenced nodes under a particular diffusion model. The influence maximization problem has been proven to be NP-hard, and most proposed solutions to the problem are approximate greedy algorithms, which can guarantee a tunable approximation ratio for their results with respect to the optimal solution. The state-of-the-art algorithms are based on Reverse Influence Sampling (RIS) technique, which can offer both computational efficiency and non-trivial (1-1/e-ϵ)-approximation ratio guarantee for any epsilon >0ϵ>0....