A method performed at a network element, the method comprising: receiving a packet that includes packet metadata; identifying a hop number for the network element; identifying a unique identifier for the network element; identifying a predetermined path identifier from the packet metadata, wherein the predetermined path identifier is indicative of a path of network elements traversed by the packet, the path including one or more other network elements; determining an updated path identifier based at least in part on the predetermined path identifier, the hop number and the unique identifier, wherein determining the updated path identifier comprises one of: calculating a path identifier value equal to the unique identifier raised to the hop number; or calculating a new path identifier value equal to a product of a previously identified path identifier value stored in a field of the packet metadata and the unique identifier raised to the hop number; or calculating a path identifier value equal to a sum of a previously identified path identifier value and a logarithm of the unique identifier multiplied by the hop number, wherein the updated path identifier is indicative of an updated path of network elements traversed by the packet, the path including the one or more other network elements and the network element; augmenting the packet metadata with the updated path identifier to provide augmented metadata; and transmitting the packet with the augmented metadata to a next network element. receiving a packet that includes packet metadata; identifying a hop number for the network element; identifying a unique identifier for the network element; identifying a predetermined path identifier from the packet metadata, wherein the predetermined path identifier is indicative of a path of network elements traversed by the packet, the path including one or more other network elements; determining an updated path identifier based at least in part on the predetermined path identifier, the hop number and the unique identifier, wherein determining the updated path identifier comprises one of: calculating a path identifier value equal to the unique identifier raised to the hop number; or calculating a new path identifier value equal to a product of a previously identified path identifier value stored in a field of the packet metadata and the unique identifier raised to the hop number; or calculating a path identifier value equal to a sum of a previously identified path identifier value and a logarithm of the unique identifier multiplied by the hop number, calculating a path identifier value equal to the unique identifier raised to the hop number; or calculating a new path identifier value equal to a product of a previously identified path identifier value stored in a field of the packet metadata and the unique identifier raised to the hop number; or calculating a path identifier value equal to a sum of a previously identified path identifier value and a logarithm of the unique identifier multiplied by the hop number, wherein the updated path identifier is indicative of an updated path of network elements traversed by the packet, the path including the one or more other network elements and the network element; augmenting the packet metadata with the updated path identifier to provide augmented metadata; and transmitting the packet with the augmented metadata to a next network element.