Topology Discovery for Virtual Local Area Networks

In this paper we investigate the problem of finding the physical layer topology of large, heterogeneous networks that comprises multiple VLANs and may include uncooperative network nodes. We prove that finding a layer-2 network topology for a given incomplete input is an NP-hard problem even when the network comprises only two VLANs and the network contains one loop and deciding whether a given input defines a unique VLANs topology is a co-NP-hard problem. We design several heuristic algorithms to find VLANs topology. Our first algorithm is designed for geographically wide-spread networks that may contain uncooperative devices. For such networks the algorithm discovers the topology for each VLAN then merges them to infer the network topology in O(n^3) time, where $n$ is the number of internal network nodes. Our second algorithm is designed for smaller, active networks where each device in the network provides access to their MIB and few AFT entries are missing. For such networks, the algorithm finds the unique topology of VLANs in O(n^3) time. We have implemented both the algorithms described in this paper and conducted extensive experiments on multiple networks. Our experiments demonstrate that our approach is quite practical and discovers the accurate VLANs topology of large and heterogeneous networks whose input may not necessarily be complete. To the best of our knowledge, this is the first paper investigating topology discovery for VLANs.