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 S 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  

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... 

The problem of finding the expected shortest path in stochastic networks, where the presence of each node is probabilistic and the arc lengths are random variables, have numerous applications, especially in communication networks. The problem being NP-hard we use an ant colony system (ACS) to propose a metaheuristic algorithm for finding the expected shortest path. A new local heuristic is formulated for the proposed algorithm to consider the probabilistic nodes. The arc lengths are randomly generated based on the arc length distribution functions. Examples are worked out to illustrate the applicability of the proposed approach  

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... 

We are concerned with the design of a model and an algorithm for computing the shortest path in a network having various types of fuzzy arc lengths. First, a new technique is devised for the addition of various fuzzy numbers in a path using α-cuts by proposing a least squares model to obtain membership functions for the considered additions. Due to the complexity of the addition of various fuzzy numbers for larger problems, a genetic algorithm is presented for finding the shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Examples are worked out to illustrate the applicability of the proposed approach  

We propose an approach for finding an optimal path in a flexible jobshop manufacturing system considering two criteria of time and cost. With rise in demands, advancement in technology and increase in production capacity, the need for more shops persists. Therefore, a flexible jobshop system has more than one shop with the same duty. The difference among shops with the same duty is in their machines with various specifications. A network is configured in which the nodes are considered to be the shops with arcs representing the paths among the shops. An automated guided vehicle functions as a material handling device through the manufacturing network. To account for uncertainty, we consider... 

In this paper, we introduce a new version of the shortest path problem appeared in many applications. In this problem, there is a start point s, an end point t, an ordered sequence =(S0 = s, S1,...,S k, Sk+1 = t) of sets of polygons, and an ordered sequence =(F0,...,Fk) of simple polygons named fences in such that each fence Fi contains polygons of Si and Si+1. The goal is to find a path of minimum possible length from s to t which orderly touches the sets of polygons of in at least one point supporting the fences constraints. This is the general version of the previously answered Touring Polygons Problem (TPP). We prove that this problem is NP-Hard and propose a precision sensitive FPTAS... 

We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective problems. The first and second approaches are extensions of the labeling method to solve the single objective problem and the third approach is based on dynamic programming. The labeling methods usually producing several nondominated paths, we propose a fuzzy number ranking method to determine a fuzzy shortest path. Illustrative examples are worked out to show the effectiveness of our algorithms  

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using α -cuts by proposing a linear least squares model to obtain membership functions for the considered additions. Then, using a recently proposed distance function for comparison of fuzzy numbers. we propose a new approach to solve the fuzzy APSPP using of genetic algorithm. Examples are worked out to illustrate the applicability of the proposed model  

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  

Traffic assignment is a step of travel demand estimation. Given a trip origin-destination demand matrix, this step determines traffic flow in each link, according to assumptions based on the behavior of drivers. Conventional assignment algorithms, which are mostly based on the Wardrop first principle of user equilibrium, assume that all drivers choose the shortest path to the destination, based on the same travel time computed by travel time functions. However, in reality, driver perception of travel time varies for a specific route. This paper presents a traffic assignment algorithm which assumes that driver perception of travel time affects route choices. Fuzzy set theory is used to define... 

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... 

We propose an approach for finding an optimal path in a flexible jobshop manufacturing system considering two criteria of time and cost. With rise in demands, advancement in technology, and increase in production capacity, the need for more shops persists. Therefore, a flexible jobshop system has more than one shop with the same duty. The difference among shops with the same duty is in their machines with various specifications. A network is configured in which the nodes are considered to be the shops with arcs representing the paths among the shops. An Automated Guided Vehicle (AGV) functions as a material handling device through the manufacturing network. To account for uncertainty, we... 

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using α-cuts. Then, we propose a regression model for obtaining membership function for the considered addition. Finally, we present a dynamic programming method for finding a shortest path in the network. An example is worked out to illustrate the applicability of the proposed approach  

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using α-cuts by proposing a linear least squares model to obtain membership functions for the considered additions. Then, using a recently proposed distance function for comparison of fuzzy numbers, we present a dynamic programming method for finding a shortest path in the network. Examples are worked out to illustrate the applicability of the proposed model  

This paper proposes a method to solve shortest path problems in route choice processes when each link's travel time is a fuzzy number, called the Perceived Travel Time (PTT). The PTT is a subjective travel time perceived by a driver. The algorithm solves the fuzzy shortest path problem (FSPA) for drivers in the presence of uncertainty regarding route travel time. For congested networks, the method is able to find the shortest path in terms of perceived travel time and degree of saturation (congestion) along routes at the same time. The FSPA can be used to support the fuzzification of traffic assignment algorithms. The applicability of the resulting FSPA for the traffic assignment was tested...