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Knowledge of both, the up-to-date physical topology of an IP network and provisioned services in a core data or optical network, is crucial to a number of critical network management tasks, including reactive and proactive resource management, event correlation, and root-cause analysis. Given the dynamic nature of today's networks, keeping track of physical and service topology information manually is a daunting (if not impossible) task. Thus, effective algorithms for automatically discovering network topology are necessary. We present novel algorithms for (a) discovering physical topology in heterogeneous (i.e., multivendor) IP networks, and (b) discovering service topology in core data or optical networks. Our algorithms for physical topology of IP networks rely on standard SNMP MIB information that is widely supported by modern IP network elements. We have implemented the algorithms presented in This work in the context of the Netlnventory topology discovery tool that has been tested on Lucent's own research network. The experimental results clearly validate our approach, demonstrating that our tool can consistently discover the accurate physical and service topology with reasonably small running-time requirements even for fairly large network configurations.