Packet Transmission Problem (PTP) and Job Scheduling Problems (JSP) are known NP-complete problems. It is also known that any NP-complete problem can be transformed into another NP-complete problem within polynomial time.
Question: How would you transform the PTP to JSP?
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Following are the descriptions of PTP and JSP. Packet Transmission Problem (PTP) There is a data packet that needs to be transmitted to all n sites on the network. Data packet cannot be duplicated by any sites, and each site should receive the data packet only once. The time it takes to transmit this data packet from site i to site j is T(i,j). PTP is to choose the routing so that this data packet can be transmitted to all sites with the least amount of time. Job Scheduling Problems (JSP) We have a set of n jobs with the amount of time they need to complete, t1, t2, …, tn, the deadline they need to be completed by, d1, d2, …, dn, and a penalty incurred if the job is not completed by the deadline, p1, p2, …, pn. JSP attempts to order this set of n jobs to incur the smallest penalty.
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