Sharif Digital Repository

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... 

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... 

An stochastic version of the classical shortest path problem whereby for each node of a graph, a probability distribution over the set of successor nodes must be chosen so as to reach a certain destination node with minimum expected cost. In this paper, we propose a new algorithm based on Particle Swarm Optimization (PSO) for solving Stochastic Shortest Path Problem (SSPP). The comparison of our algorithm with other algorithms indicates that its performance is suitable even by the less number of iterations. © 2008 Springer-Verlag Berlin Heidelberg  

We study a constrained version of the shortest path problem in polygonal domains, in which the path must visit a given target polygon. We provide an efficient algorithm for this problem based on the wavefront propagation method and also present a method to construct a subdivision of the domain to efficiently answer queries to retrieve the constrained shortest paths from a single-source to the query point. © 2008 Springer-Verlag Berlin Heidelberg  

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  

The critical issue in designing correlated data networks like Wireless Sensor Networks is to minimize the total cost of data transmission in the network, and decrease the amount of data flow. The problem of finding optimal aggregation tree for correlated data gathering in single sink network is considered as an NP-Complete problem and hence heuristic methods are usually applied to solve it[1]. In this paper, we apply genetic algorithm (GA) to solve the problem. In our method, we improve the performance of genetic search by selecting proper initial population. This initial population is determined in two ways, by using Prime's algorithm, and shortest path tree. The main issue is to regard... 

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... 

In this paper we consider maintaining the visibility of a segment observer moving inside a simple polygon. A practical instance of this problem is to identify the regions of a planar scene illuminated by a fluorescent lamp while the lamp moves around. We consider both strong and weak visibility in this paper. Our method is based on the shortest path tree which builds a linear-sized data structure in O(n) time, where n is the number of the vertices of the underlying simple polygon P. We first compute VP(st̄), the initial view of the segment observer st̄. Then, as st̄ moves, each change of VP(st̄) can be computed in O(log2(|V P(st̄)|)) time when the observer is allowed to change its direction,... 

The shortest path problem is a classical and important network optimization problem appearing in many applications. We discuss the shortest path problem from a specified vertex to every other vertex on a network with imprecise arc lengths as fuzzy numbers. Using an order relation between fuzzy numbers, we propose a new algorithm to deal with the fuzzy shortest path problem. The algorithm is composed of a fuzzy shortest path length procedure and a similarity measure. The fuzzy shortest length method is proposed to find the fuzzy shortest length, and the fuzzy similarity measure is utilized to get the shortest path. Two illustrative examples are worked out to demonstrate the proposed algorithm... 

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... 

In this paper, we consider acyclic networks of queues as a model to support the design of a dynamic production system. Each service station in the network represents a manufacturing or assembly operation. Only one type of product is produced by the system, but there exist several distinct production processes for manufacturing this product, each one corresponding with a directed path in the network of queues. In each network node, the number of servers in the corresponding service station is either one or infinity. The service time in each station is either exponentially distributed or belongs to a special class of Coxian distribution. Only in the source node, the service system may be... 

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... 

By applying shortest path analysis in stochastic networks, we introduce a new approach to obtain the reliability function of time-dependent systems. 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 that 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 stochastic network... 

We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. We provide a worst-case optimal algorithm for this problem and also present a method to construct a subdivision of the simple polygon to efficiently answer queries to retrieve the shortest polygon-meeting paths from a single-source to the query point. The algorithms are linear, both in time and space, in terms of the complexity of the two polygons. © 2004 Elsevier B.V. All rights reserved