Sharif Digital Repository

In the Touring Polygons Problem (TPP) there is a start point s, a sequence of simple polygons P=(P1,. . .,Pk) and a target point t in the plane. The goal is to obtain a path of minimum possible length that starts from s, visits in order each of the polygons in P and ends at t. This problem was introduced by Dror, Efrat, Lubiw and Mitchell in STOC '03. They proposed a polynomial time algorithm for the problem when the polygons in P are convex and proved its NP-hardness for intersecting and non-convex polygons. They asked as an open problem whether TPP is NP-hard when the polygons are pairwise disjoint. In this paper, we prove that TPP is also NP-hard when the polygons are pairwise disjoint in... 

Give a triangulation of a set of points on the plane, dilation of any two points is defined as the ratio between the length of the shortest path of these points and their Euclidean distance. Minimum dilation triangulation is a triangulation in which the maximum dilation between any pair of the points is minimized. We give upper bounds on the dilation of the minimum dilation triangulation for two kinds of point sets: An upper bound of nsin⁡(π/n)/2 for a centrally symmetric convex point set containing n points, and an upper bound of 1.19098 for a set of points on the boundary of a semicircle. © 2018 Elsevier B.V  

In this paper, we investigate an efficient deadlock-free shortest path routing algorithm for WK-recursive mesh networks which has been shown that possess several advantages like suitable to be manufactured by VLSI technology and easy to be expanded. It will be shown that the proposed algorithm requires O(√n) routing steps (where N is the network size) to route the entire network by exploiting either the self-routing or second order routing scheme. © Springer-Verlag Berlin Heidelberg 2008  

In this paper, we study the problem of finding the shortest path between two points inside a simple polygon such that there is at least one point on the path from which a query point is visible. We provide an algorithm which preprocesses the input in O (n2 + n K) time and space and provides logarithmic query time. The input polygon has n vertices and K is a parameter dependent on the input polygon which is O (n2) in the worst case but is much smaller for most polygons. The preprocessing algorithm sweeps an angular interval around every reflex vertex of the polygon to store the optimal contact points between the shortest paths and the windows separating the visibility polygons of the query... 

By applying shortest path analysis in stochastic networks, we introduce a new approach to obtain the reliability function of time-dependent systems with standby redundancy. We assume that not all elements of the system are set to function from the beginning. Upon the failure of each element of the active path in the reliability graph, the system switches to the next path. Then, the corresponding elements are activated and consequently the connection between the input and the output is established. It is also assumed each element exhibits a constant hazard rate and its lifetime is a random variable with exponential distribution. To evaluate the system reliability, we construct a directed... 

We consider the problem of walking in an unknown street, starting from a point s, to reach a target t by a robot which has a minimal sensing capability. The goal is to decrease the traversed path as short as possible. The robot cannot infer any geometric properties of the environment such as coordinates, angles or distances. The robot is equipped with a sensor that can only detect the discontinuities in the depth information (gaps) and can locate the target point as soon as it enters in its visibility region. In addition, a pebble as an identifiable point is available to the robot to mark some position of the street. We offer a data structure similar to Gap Navigation Tree to maintain the... 

This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously published bounds. The connection-graph-stability score for each edge is defined as the sum of the lengths of the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is bounded below by the size of the graph divided by the maximum connection-graph-stability score assigned to the edges  

Let P be a set of n points inside a polygonal domain D. A polygonal domain with h holes (or obstacles) consists of h disjoint polygonal obstacles surrounded by a simple polygon which itself acts as an obstacle. We first study t-spanners for the set P with respect to the geodesic distance function π where for any two points p and q, (p, q) is equal to the Euclidean length of the shortest path from p to q that avoids the obstacles interiors. For a case where the polygonal domain is a simple polygon (i.e., h = 0), we construct a (10 + ε)-spanner that has O(n log2 n) edges. For a case where there are h holes, our construction gives a (5 + ε)-spanner with the size of O(nh log2 n). Moreover, we... 

We have constructed a collaboration network for physicists based in Iran working in different disciplines. By discussing properties like collaborators per author, shortest path, betweenness, and the concept of power in networks for this local model, and comparing with the global model, we understand how a developing country in the Middle East is contributing to the scientific growth in the world statistically. In this comparison, we found some properties of the local model which were not in accordance with the standard global society of science, which should be considered in developing the future policies. Our results show significant differences in factors like the degree and the diameter... 

Nowadays development of cell phone network provides huge and ubiquitous data, with wide application in transportation science. One of the most important advantages of these kinds of data is enabling the process of collecting information without any active users' interference. A big data set consisting of 300,000 cell phone users' information in Shiraz are studied. This data set includes spatiotemporal information of travelers for every 5 minutes in a time span of 40 hours in two consecutive days. The spatial part of each user's information contains the position of the BTS (Base Transceiver Station) to which his cell phone is currently connected. Due to the existence of outliers, it is... 

We study the problem of finding a target t from a start point s in street environments with the cooperation of two robots which have a minimal sensing capability; that is, robots do not know any information about the workspace including information on distances, edges, coordinates, angles etc. They just can detect the discontinuities in the visibility region of their location. The robots can detect target point t as soon as it enters their visibility region and have communication peripherals to send messages to each other. Our aim is to minimize the length of the path passed by the robots. We propose an online algorithm for robots such that they move in the workspace and find the target....