To avoid the potential problem of network messages (packets) looping around forever inside a network, each message includes a Time To Live (TTL) field. This field contains the number of nodes (stations, computers, etc.) that can retransmit the message, forwarding it along toward its destination, before the message is unceremoniously dropped. Each time a station receives a message it decrements the TTL field by 1. If the destination of the message is the current station, then the TTL field’s value is ignored. However, if the message must be forwarded, and the decremented TTL field contains zero, then the message is not forwarded.
In this problem we are given the description of a number of networks, and for each network we are asked to determine the number of nodes that are not reachable given an initial node and TTL field value. Consider the following example network:
If a message with a TTL field of 2 was sent from node 35 it could reach nodes 15, 10, 55, 50, 40, 20 and 60. It could not reach nodes 30, 47, 25, 45 or 65, since the TTL field would have been set to zero on arrival of the message at nodes 10, 20, 50 and 60. If we increase the TTL field’s initial value to 3, starting from node 35 a message could reach all except node 45
Mandip Sibakoti, ’12 Kathmandu, Nepal
Major: Computer Science
Sponsor: Leon Tabak