Achieving maximum flow for Inter-planetary networks

Inter-planetary network (IPN) systems on earth and spacecrafts communicate with systems on other planets. Communications and data are often relayed and delivered by the IPN systems. Delay/Disruption Tolerant Networking (DTN) have several unique characteristic features with significant challenges such as intermittent link connectivity, long and variable propagation delays, link bandwidth asymmetry, high link error rates and Power constraints. It is vital to overcome these challenges to achieve maximum flow for IPN systems. The aim of this project is to address the issue of achieving maximum flow in Inter-planetary network. To tackle these issues, a DTN model as time aggregated graph (TAG) was proposed and a bidirectional storage transfer series was used to correlate various time intervals and aid in maximizing flow. Our results suggest that the maximum flow can be achieved by seeking an augmenting path, computing its maximum flow, and getting its residual network using an iterative approach. In future, we intend to investigate the increase in difficulty of achieving maximum flow.

Maximum Network Flow Algorithms

The aim of the maximum network flow problem is to push as much flow as possible between two special vertices, the source and the sink satisfying the capacity constraints. For the solution of the maximum flow problem, there exists a number of algorithms. The existing algorithms can be divided into two families. First, augmenting path algorithms that satisfy the conservation constraints at intermediate vertices and the second preflow push relabel algorithms that violates the conservation constraints at the intermediate vertices resulting incoming flow more than outgoing flow.In this paper, we study different algorithms that determine the maximum flow in the static and dynamic networks.

An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

This paper presents an algorithm for solving a minimum cost flow (MCF) problem with a dual approach. The algorithm holds the complementary slackness at each iteration and finds an augmenting path by updating node potential iteratively. Then, flow can be augmented at the original network. In contrast to other popular algorithms, the presented algorithm does not find a residual network, nor find a shortest path. Furthermore, our algorithm holds information of node potential at each iteration, and we update node potential within finite iterations for expanding the admissible network. The validity of our algorithm is given. Numerical experiments show that our algorithm is an efficient algorithm for the MCF problem, especially for the network with a small interval of cost of per unit flow.

Computer algorithms

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

Augmenting trail theorem for the maximum 1-2 matching problem

We consider the maximum 1-2 matching problem in bipartite graphs. The notion of the augmenting trail for the 1-2 matching problem, which is the extension of the notion of the augmenting path for the 1-1 matching problem is introduced. The main purpose of the present paper is to prove “the augmenting trail theorem” for the 1-2 matching problem in the bipartite graph, which is an analogue of the augmenting path theorem by Bergé for the usual 1-1 matching problems.