1. [15 pts] Suppose a program takes 10000 seconds to run on single processor system. However, the parallel version of the program takes only 3200 seconds to run on a four processor (four core) system. a) Find the speed up of the parallel program over the serial one. b) The parallel program runs for a while in a serial mode and then in a parallel node. Find out the time the program spends in the serial mode of execution. 2. [15 pts] Suppose a program must execute 1017 instructions to solve a particular problem. Suppose further that a single processor system can solve the problem in 10 seconds. So, on averuge, the single processor system executes 10 instructions per second. Now suppose that the program has been parallelized for execution on a distributed-memory system Suppose also that if the parallel program usces p processors, cach processor will execute 1012/p instructions and each processor must send 109(p1) messages. Finally, suppose that there is no additional overhead in executing the parallel program. That is, the program will complete after each processor has executed all of its instructions and sent all of its messages, and there won't be any delays due to things such as waiting for messages. a. Suppose it takes 109 seconds to send a message. How long will it take the program to run with 100 processors, if each processor is as fast as the single processor on which the serial program was run? b. Suppose it takes 103 seconds to send a message. How long will it take the program to run with 100 processors?s 3. [10 pts] Derive the formula for the total number of links for each of the interconnection networks in terms of n where is the number of processors connected on the network: a) Fully connected b) Hypercube 4. [10pts] Suppose Tostai =n and Tp=nitel=n/p+log(p), where times Twmi and Tpmonil are in microseconds. Assume p represents the number of processes. a) Write the expressions for speed up and efficiency. b) Find the speedup and efficiency for n=10000 and p=16