978-1-4244-9730-0/10/$26.00 ©2010 IEEE Hopfield Neural Network for Disjoint Path Set Selection in Mobile Ad-hoc Networks Ehsan Hemmati #*1 , Mansour Sheikhan #2 # Department of Electrical Engineering, Islamic Azad University South Tehran Branch, Teheran, Iran * Young Researchers Club 1 ehsan@hemmati.info 2 msheikhn@azad.ac.ir Abstract—Topological changes in Mobile Ad-hoc NETwork (MANET) render routing paths unusable. Using multiple redundant paths between the source and the destination is a technique which reduces the affect of this problem. Shared links and nodes between paths present common failure points which can disable many or all of the paths. Disjoint path set requires the multiple paths to be link- or node-disjoint. However, selecting an optimal path set is an NP-complete problem. Neural networks have been proposed as computational tools for solving constrained optimization problems. A Hopfield neural network is proposed as a path set selection algorithm in this paper. This algorithm is beneficial for mobile ad-hoc networks, since it produces a set of backup paths with high reliability. This approach can find either node-disjoint or link-disjoint path set with no extra overhead. Keywords— mobile ad-hoc network; path set selection; neural network; reliability; I. INTRODUCTION Mobile Ad-hoc Networks (MANET) are networks based neither on a base station nor any kind of fixed infrastructure. These networks are useful when no wired link is available such as in disaster recovery or more generally when a fast deployment is necessary. Network tasks like relaying packets, discovering routes, monitoring the network, securing communication, etc are performed by mobile nodes in this network. Nodes typically communicate in multi-hopping fashion [1], [2]. Intermediate nodes act as routers by forwarding data. Topology of ad-hoc network is highly dynamic because of mobility and limited battery power of nodes. Routing protocols should adapt to such dynamism, and continue to maintain connection between the source and destination nodes in the presence of path breaks caused by mobility and/or node failures. Single-path routing algorithms cause long network latencies and excessive overhead when paths fail. A promising approach is to use not just a single path, but a set of redundant paths, to mask failures in the network [3]. There is a fundamental, and quite difficult, question: which of the potential exponentially many paths within the network should the routing layer use to achieve the highest reliability? In order to have high reliable path set, the correlation of failures between the paths in the set should be as low as possible. Common links and nodes between paths are common failure points in the set. In order to provide high reliable path set, we should find disjoint paths. The problem of finding disjoint paths is non-trivial. Two general principles for selecting a reliable path set can be easily stated. First, a long path is less reliable than a short one. And second, a larger number of disjoint paths increases the overall reliability. Thus, in general, one should be looking for a large set of short and disjoint paths. The problem of finding the most reliable path set has already been shown to be computationally hard [4]. One of the important applications of neural network is to solve optimization problems. In these cases, we want to find the best way to do something, subject to certain constraints. Hopfield neural network is a model that is commonly used to solve optimization and NP-complete problems [5], [6]. One of the most important features of this model is that Hopfield network can be easily implemented in hardware, therefore neuron computations are performed in parallel and the solution is found more quickly. In this paper, we introduce a Hopfield network model to find the most reliable path set in a MANET. Each node in the network can be equipped with a neural network, and all network nodes can train and use the neural networks to obtain optimal or near-optimal disjoint path set. II. HOPFIELD NEURAL NETWORK The use of neural networks to solve constrained optimization problems was initiated by Hopfield and Tank [5], [6]. In a Hopfield neural network connectivity between neurons represented by an n×n weight matrix, W=[W ij ], with the restriction that W ij =W ji and W ii =0. A sigmoid monotonic increasing function relates the output V i of the i th neuron to its input U i . The range of output V i is between 0 and 1. A typical sigmoid transfer function is given by: . 1 ( ) 1 i i i i i U V g U e λ - = = + (1) In this model, each neuron receives an external current (known also as a bias) I i . Hopfield networks dynamic can be described as follows [7]: 1 N i i ij j i j dU U W V I dt τ = = ⋅ - + ∑ (2)