HOMEWORK 1:  Pseudocode, enumerative algorithms, and combinatorical problems
 

Handed out/Assigned:	Friday,Sept. 8, 2000
Due:	Wednesday, Sept. 13, 2000

Write pseudocode to solve one of the three problems we discussed in class.   Use an enumerative, exhaustive approach that guarantees the optimal answer will be found.
 

1. New York City Tunnels Problem (pipe network design):
• p = 21 pipes,  d = 16 diameters possible for each pipe.
• Thus can use 4 bits for each pipe, times 21 yields 84 bits total binary represenation of decision variables.
• Assume a function called simulate(pipe_design) that takes as input a pipe network design (e.g., setting of the 84 bits, or an array of 21 integers from 0..15 each, whatever) and returns a floating point cost, which you are trying to minimize.
• Write the loops, or recursions, or whatever, to examine the entire search space, keeping track of the lowest cost solution found so far.
• Specify, abstractly, a data structure for the pipes and diameters.  (e.g., a binary string, or a list of integers, etc.)
• Roughly analyze the run-time of your algorithm, in terms of input sizes p and d.
2. Groundwater Monitoring (subset selection)
• There are w = 396 possible well sites.  You must choose k=20 of them.
• Assume a function called simulate(wells), that takes as input a collection of 20 different wells,  and outputs a floating point value for the subsequent capture_rate, which you are trying to maximize.
• Write the loops, or recursions, or whatever, to examine the entire search space, keeping track of the highest capture rate found so far.
• Specify, abstractly, a data structure for the well sites and wells.
• Roughly analyze the run-time of your algorithm, in terms of input sizes w and k.
3. Task Scheduling
• You have t unique tasks to schedule linearly (i.e., a single, complete ordering).
• Assume a function called simulate(schedule) that takes as input an ordering of the t tasks and outputs a floating point profit, to be maximized.
• Write the loops, or recursions, or whatever, to examine the entire search space, keeping track of the highest profitsolution found so far.
• Specify, abstractly, a data structure for the ordering of the tasks
• Roughly analyze the run-time of your algorithm, in terms of input size t.