This paper presents an adaptive amoeba algorithm to address the shortest path tree (SPT) problem in dynamic graphs. In dynamic graphs, the edge weight updates consists of three categories: edge weight increases, edge weight decreases, the mixture of them. Existing work on this problem solve this issue through analyzing the nodes influenced by the edge weight updates and recompute these affected vertices. However, when the network becomes big, the process will become complex. The proposed method can overcome the disadvantages of the existing approaches. The most important feature of this algorithm is its adaptivity. When the edge weight changes, the proposed algorithm can recognize the affected vertices and reconstruct them spontaneously. To evaluate the proposed adaptive amoeba algorithm, we compare it with the Label Setting algorithm and Bellman-Ford algorithm. The comparison results demonstrate the effectiveness of the proposed method. The shortest path tree problem (SPT) is one of the basic network optimization problems and it is a variance of the shortest path problem (SPP), which has been widely used in many fields, such as multicast routing, 1 Route Information Protocol (RIP), 2 wireless network, 3 network design, 4, 5 IS-IS, 6 and complex networks. 7-9 Its objective is to find the set of edges which connect all the nodes in the network so that the sum of the edge lengths from the source to the other nodes is minimized. As the SPT problem is frequently as subproblem when solving many combinatorial and network optimization problems, many researchers payed their attention to this problem. In practical environment, the network is changing with time. It lead to the occurence of the variance of SPTs named Dynamic Shortest Path (DSP) problem. Assume G (V, E, ω) be a simple network and the edge weights in this network are nonnegative numbers. Let G 12 and Bellman algorithm solve this problem through recalculating the SPTs whenever there is a change to edge weights. Due to the high computational time, it cannot meet the requirement of the emergent accidents. After the idea of using an SPTs update program which only reconstruct on the affected vertices proposed by Frigioni 13 appeared, many dynamic SPTs approaches have implemented this concept into realworld applications 10, 11 to reduce the computational time. They have divided the edge weight updates into three categories: edge weight increase, edge weight decreases, the mixture of them. For the edge updates belonging to different categories, various operations are processed. The main feature of these approaches is recognize the
Zhang et al. REF used this property to solve dynamic shortest path problems.
An Adaptive Amoeba Algorithm for Shortest Path Tree Computation in Dynamic Graphs
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Computer Science Mathematics