Download Autumn Examinations 2011 - Computer Science (COMP 8011) - Graph Theory Problems and more Exams Computer Science in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2010/
Module Title: Computer Science
Module Code: COMP 8011
School: Science and Computing
Programme Title: Bachelor of Science (Honours) in Software Development – Award
Programme Code: KSDEV_8_Y
External Examiner(s): Ms. A. Meagher Internal Examiner(s): Dr. J. Stynes
Instructions: Answer Question 1 and 3 others. Show all work.
Duration: 2 Hours
Sitting: Autumn 2011
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1 Provide a graph model for each of the following problems and then solve the problem. The solution MUST be obtained by using a graph theory result. (a) Can everyone in a group of 11 people know exactly 3 others in the group? Do the same with 8 people. (5 marks) (b) Consider the problem of scheduling 7 exams in 7 days, one exam per day and no two exams in the same course fall on consecutive days. If no course has more than 4 exams, show that this can be done. (5 marks) (c) Given four houses and four utility poles, can each house be connected to each utility pole in such a way that none of the connecting wires cross? (5 marks) (d) The management structure in organization X is a tree structure, in which every manager manages 4 people and may have another manager managing him/herself. If the organization has 865 employees in total, how many employees are not managers? (5 marks) (e) Jane is in charge of assigning part-time jobs at a college. She has 30 student applications and there are 30 part-time jobs. Each applicant is qualified for at least 5 jobs but each job can be performed by at most 4 applicants. Can Jane assign all students to jobs for which they are qualified? (6 marks) (f) John is holding a party and has invited 10 people. The 11 people at the party are all acquainted with exactly 6 others. Can John seat them at a round table in such a way that everybody has someone that he/she is acquainted with on either side? (6 marks) (g) A set of experiments are to be made at observatories. Each experiment begins on a given day of the year, and ends on a given day. Each experiment is repeated for several years. An observatory can perform only one experiment at a time. What is the minimum number of observatories needed to perform a given set of experiments annually given the following data? Experiment A runs from Sept. 2 to Jan. 3, experiment B runs from Oct. 15 to March 10, experiment C from Nov. 20 to Feb. 17, D from Jan 23 to May 30, E from April 4 to July 28, F from April 30 to June 28, G from June 24 to Sept 30. (8 marks)
Q5 (a) Find a Hamilton cycle in the graph K (Figure 3), or prove using the “3 rules” method that no Hamilton Cycle exists. (8 marks) (b) Analyse the complexity of the recursive function func assuming S 1 and S 2 are blocks of code of complexity O(1). int func( int n ) { if ( n = = 1 ) S 1 ; //S 1 is O(1) else if ( n = = 2) S 2 ; //S 2 is O(1) else return( 3 func(n-1) + 2 func(n-2); }** (12 marks)
Figure 1 (graph G)
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Figure 3 (Graph K)
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