Determining All Minimal Paths of a Network (original) (raw)
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An Algorithm to Search for All Minimal Cuts in a Flow Network
Advances in systems science and applications, 2020
Reliability evaluation approaches exploit a variety of tools for system modeling and calculation of reliability indices. Most proposed approaches in the literature are in terms of minimal cuts (MCs) or minimal paths. Hence, finding all the MCs in a network is an attractive problem in network flow and reliability theory. Here, investigating some works related to the MC problem, we first point out a number of defects in certain proposed algorithms, and present certain new techniques to rectify the flaws in two algorithms. Moreover, we present some techniques to improve the algorithms. Using our results, we propose an improved algorithm for finding all the MCs in a flow network. A benchmark network example is used to illustrate the performance of the algorithm. The proposed algorithm is shown to be correct. Finally, after establishing the complexity results, we demonstrate the proposed algorithm to be more efficient than some existing algorithms.
An Efficient Algorithm for Enumerating all Minimal Paths of a Graph
International Journal of Advanced Computer Science and Applications, 2019
The enumeration of all minimal paths between a terminal pair of a given graph is widely used in a lot of applications such as network reliability assessment. In this paper, we present a new and efficient algorithm to generate all minimal paths in a graph G(V, E). The algorithm proposed builds the set of minimal paths gradually, starting from the source node s. We present two versions of our algorithm; the first version determines all feasible paths between a pair of terminals in a directed graph without cycle, and this version runs in linear time O(|V | + |E|). The second version determines all minimal paths in a general graph (directed and undirected graph). In order to show the process and the effectiveness of our method, an illustrative example is presented for each case.
The mathematical theory of reliability has grown out of the demand of modern technology and particularly out of the experience with complex systems. The main objective is to enhance the ability of such complex network systems. This work present an efficient algorithm, which is a novel approach to generate all the minimal paths of the general flow network based on the principle of backtracking. It is a general flow network because, the proposed approach can find the minimal paths for multiple sources and multiple sinks in the network. One can further evaluate the network reliability using any existing SDP (Sum of Disjoint Products) based approach.
Research Paper on Finding All Paths and Critical Nodes in a Network
Multipath Routing and critical node are two main factors that play very important role in network performance. In this paper multipath and critical nodes in a network are discovered. Multipath routing is the technique of choosing multiple alternate paths within a network, which gives a variety of benefits such as increased bandwidth, improved security or fault tolerance. The multiple paths computation may be overlapped, node-disjointed or edge-disjointed with each other. A Critical node is node whose in degree and out degree is greater than other nodes. That node is treated as a critical node because if all nodes connected to that critical node try to send data at the same time it degrades the performance of network, so to overcome this problem multipath concept is introduced. In this dissertation there is a discussion of such critical nodes. To discover allpath and critical nodes a program is implemented in MatLab. Algorithm of program and flow chart of algorithm are also discussed. An algorithm has been proposed to find all paths and critical nodes in network.
A NEW ALGORITHM FOR FINDING ALL MINIMAL CUTS IN MODIFIED NETWORKS
Evaluating network reliability is an important topic in the planning, designing and control of network systems. Modifications are common for network expansion or reinforcement evaluation and planning. A modified network is an updated network after inserting a branch string (a special path) between two nodes in the original network. The problem of searching all minimal cuts (MCs) in a modified network is discussed and solved in this study. The proposed algorithm is easier to understand and implement than the existing known related algorithms. The accuracy of the proposed algorithm will be validated. The computational complexity of the proposed algorithm is analyzed and compared with the existing best-known methods. One benchmark example is illustrated to show how to find all MCs in a modified network using the information of all the MCs in the corresponding original network.
Enumeration of the minimal node cutsets based on necessary minimal paths
IAES International Journal of Artificial Intelligence (IJ-AI), 2020
Reliability evaluation is an important research field for a complex network. The most popular methods for such evaluation often use Minimal Cuts (MC) or Minimal paths (MP). Nonetheless, few algorithms address the issue of the enumeration of all minimal cut sets from the source node s to the terminal node t when only the nodes of the network are subject to random failures. This paper presents an effective algorithm which enumerates all minimal node cuts sets of a network. The proposed algorithm runs in two steps: The first one is used to generate a subset of paths, called necessary minimal paths, instead of all minimal paths. Whereas, the second step stands to build all minimal cutsets from the necessary minimal paths.
IRJET- Research Paper on Finding All Paths and Critical Nodes in a Network
IRJET, 2021
Multipath Routing and critical node are two main factors that play very important role in network performance. In this paper multipath and critical nodes in a network are discovered. Multipath routing is the technique of choosing multiple alternate paths within a network, which gives a variety of benefits such as increased bandwidth, improved security or fault tolerance. The multiple paths computation may be overlapped, node-disjointed or edge-disjointed with each other. A Critical node is node whose in degree and out degree is greater than other nodes. That node is treated as a critical node because if all nodes connected to that critical node try to send data at the same time it degrades the performance of network, so to overcome this problem multipath concept is introduced. In this dissertation there is a discussion of such critical nodes. To discover allpath and critical nodes a program is implemented in MatLab. Algorithm of program and flow chart of algorithm are also discussed. An algorithm has been proposed to find all paths and critical nodes in network.
Efficient Algorithms for Reliability Evaluation of General Networks
Frontiers in Science and Engineering, 2016
Several production systems either for goods or services can be modeled by a network where nodes are production centers, warehouses, distributions and others, and arcs represent the relationship between nodes. Nodes and arcs are often subjected to random failures that may result from several causes. These networks include one or more sources and one or more destinations. Given the stochastic nature of the failure, the reliability and the robustness of the network become an important criteria for safety, economical and environment reasons. Several methods based on graph theory and stochastic processes are proposed in the literature. The concepts of minimal paths set (MPS) and minimal cuts set (MCS) as well as decomposition techniques based on Bayes' theorem have been widely used. The performance of these methods is greatly affected by network size (number of nodes and arcs) and its density. Generally, except for special structure of some networks (e.g series, parallel, standby, etc.) there is no mathematical expression based on the reliability of its nodes and its arcs that has been proved compact for representing the expression of the reliability function of any network. This paper attempts to provide solutions to this problem by proposing and testing a unified approach based on MPS/MCS and Binary Decision Diagrams (BDD). This approach is illustrated by several simple examples. A tool has been developed to handle complex networks such as telecommunication networks and other network's tests published in the literature.
A New Technique for Generating Minimal Cut Sets in Nontrivial Network
AASRI Procedia, 2013
Network reliability analysis problem is the center of many scientific productions. It consists of evaluating the all-terminal reliability of networks. Two classes have emerged; exact and approximate methods. The aim of this paper is to present an efficient exact method for enumerating minimal cuts (MCS) of R-networks. The algorithm proceeds by determining minimal paths set (MPS) and from which minimal cuts are generated by managing binary decision diagrams. The manipulation process consists of a series of transformations, reductions and filtering operations. The approach succeeds in the reduction of computation time and memory space and was applied for evaluating the reliability of a national radio communication network.
A simple algorithm to search for all MCs in networks
European Journal of Operational Research, 2006
Evaluating the network reliability is an important topic in the planning, designing, and control of systems. The minimal cut (MC, an edge set) set is one of the major and fundamental tools for evaluating the network reliability. In this study, an alternative method is given to define a MC using a node set (called MCV). A very simple algorithm based on some intuitive theorems that characterize the structure of the MCV and the relationship between MC and MCV is developed to find the MCs between two special nodes. The proposed algorithm is then generalized to find all MCs between all pairs of nodes. The proposed algorithm is not only easier to understand and implement, but is also better than the existing best-known algorithm. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all MCs are generated and verified in a network using the proposed algorithm.