Finding Ethernet-Type Network Topology is Not Easy

In this paper we investigate the problem of finding a layer2 network topology when the information available from SNMP MIB is incomplete. We prove that finding a network topology in this case is NPhard. We further prove that deciding whether the given information defines a unique network topology is a co-NP-hard problem. We show that if there is a single node r such that every other network node sees it, then the network topology can be restored in polynomial (in the number of network ports) time. Finally, we design a polynomial time heuristic algorithm to restore a topology when the information available from SNMP MIB is incomplete and conduct extensive experiments with it to determine how often the algorithm succeeds in finding topology. Our results indicate that our algorithm restores the network topology in close to 100% of all test cases.