As you all know, the decision making process may be very complicated especially when people from outside exert their influence on the person that is supposed to make the decision. This happens all the time in all places and it may have some benefits after all.
IIT, like many other private Universities, gets part of its funds from donations. It has recently launched a fund raising campign. Money will be used to repair or upgrade facilities, foster a better social life, create new scholarships. Part of the money may be used to finally put new pavement on the parking lot at State Stree and 31st (the south part that is). Anyway, to get money you need to move the proper levers. You must know who influences whom, in order to talk to the right person(s).
A brief description of the problem is given in the enclosed memorandum and in the email your instructor has received from the Chairman of the Computer Science and Applied Mathematics (CSAM) at IIT.
A theoretical introduction to the problem is given in a PostScript document you can download.
You are not required to implement the algorithm Clique. However, if you decide to do it and you succeed, then you will be rewarded with a 20% bonus.
I suggest that your program(s) handle matrices inside. At the input level I suggest that you read from a file in which each line contains a pair of numbers. The pair 3 7 for instance, would indicate that 3 influences 7.
DATE: February 1, 1996
TO: Robert Carlson, Chairman of the CSAM Department
FROM: Lew Collens, President of IIT
SUBJECT: Help needed
As you know, the University has launched an unprecedented fund-raising campaign. To avoid past mistakes we have decided to carefully learn the way our prospective donors influence each other. We have a list of such influences. For obvious reasons we use generic names insead of the real names of donors.
Since we have seen that the influence of one person does not extend beyond the second level of influencing (i.e. if D1 influences D2, D2 influences D3, and D3 influences D4, we know that working on D1 we may get some money from D2 and D3, but not from D4), we ask you to find two things:
We believe this is something the people in your department could solve using computers. Your Department recommends itself for this job through the high quality faculty and some of the finest students at this University.
Your cooperation is highly appreciated.
From carlson Mon Feb 12 12:14:34 1996 Received: by charlie.acc.iit.edu (950215.SGI.8.6.10/940406.SGI) for virgil id MAA28491; Mon, 12 Feb 1996 12:14:33 -0600 Date: Mon, 12 Feb 1996 12:14:33 -0600 From: carlson (Robert Carlson) Message-Id: <199511011814.MAA28491@charlie.acc.iit.edu> To: virgil Subject: Help Status: R Dear Virgil, As you probably know the University has launched a fund raising campaign. The President has asked our Department for assistance. In the list of influences between potential donors we must find two things: * who are the leaders (I suspect these are the people influenced by nobody) * all two-stage influences It is quite obvious that you can represent the influences as a digraph and then work on it (or in the digraph's matrix). My impression is that a leader will be a source in the digraph. As far as the two-stage influences are concerned I am sure you have either covered this in your class or you will post some information about it. Given that you have just taught relations in your class, we ask you to use your students' expertise in this matter. To be more precise, we'd like to have each student create a program that takes a digraph's matrix and outputs: * who are the leaders * all two-stage influences We really appreciate your cooperation in this matter. Sincerely, --Bob P.S. What about asking the students to also find cliques in the group?
An arrow (->) indicates the sense of the influence. D1 stands for prospective donor #1, etc.
(c) 1996, Virgil Bistriceanu
Posted February 13, 1996. Last modified February 14, 1996.
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