This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: S (Orkn‘x 20:3? Math 141 I Exam 1 Version 2 Name: ' Lecture: (circle one) I or 2 1. "We admit that this ballot measure is popular. But we also urge you to note that there are
so many bond issues on this ballot that the whole thing is getting ridiculous." What type of fallacy? Give a reason.
2. 'Tfyou're not ﬁrst you ’re last." What type of fallacy? Give a reason. 3. What is the degree of vertex A in the graph below? 4. Every graph that has an Euler circuit is connected.
A) True
B) False Page 1 5. Which of the graphs below have Euler" circuits? A) I only B) 11 only _ C) Both I and II
D) Neither I nor II 6. After a major natural disaster, such as a ﬂood, hurricane er tornado, many tasks need to
be completed as efficiently as possible. For which situation below would ﬁnding an
Euler circuit or an efﬁcient eule'rization of a graph be the appropriate mathematical
technique to apply? A) Relief food supplies must be delivered to eight emergency shelters located at
different sites in a large city. B) The Department of Public Works must inspect traffic lights at intersections in the
city to determine which are still working. C) An insurance claims adjuster must visit 10' homes in various neighborhoods to write
reports. D) The Department of Public Works must inspect all streets in the city to remove
dangerous debris.  7 7. Cousider the paths represented by the numbered sequence of edges on the graphs below.
Which path represents an Euler circuit? A) I only B) II only C) Both I and II
D) Neither I nor H Page 2 8. Which of the graphs shown below gives the best eulerization of the given graph. (In the
graphs below, added edges are denoted with zig—zag lines.) 1% ha
[LE (1% 9. In order to eulerize the graph below, give the fewest number of edges that need to be
added or duplicated? A) 1
B) '2
C) 3
D) 4 Page 3 10. Whjch of the following describes a Hamiltonian circuit for the graph below? 11. A A A C B
A) ABCDEFGA B) ACBAEGFDEA
C) ACBFGDEA
D) ABCDGEF For the graphlbelow, what is the cost of the Hamiltonian circuit obtained by using the 7
sortededges algorithm? Page 4 12. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the
nearestneighbor algorithm, starting at A? A) 215
B) 220
C) 235
D) 295 13. A hemisticaigorithm wiIl always produce optimal results.
A) True
B) False 14. Use Kruskal's algorithm for minimumcost spanning trees on the graph below. The cost
of the tree found is: 8 A. 4
A) 23
B) 20
C) 16
D) 5 Page 5 15. 16. 17. 18. Kruskal's algorithm for ﬁnding minimum—cost spanning trees always gives optimal
results. ' A) True B) False A connected graph G has 32 vertices. How many edges does a spanning tree of G have?
A) 30
B) 31
C) 32
D) 33 If the orderrequirement digraph for a collection of tasks is shown below, then What is
the minimum completion time for the collection of tasks? T1 T2 E A) 64 minutes
B) 43 minutes
C) 36 minutes
D) 28 minutes Suppose that a crew can currently complete in a minimum amount of time the job whose
orderrequirement digraph is shown below. If Task T2 is shortened from 9 minutes to 6
minutes, then What is the maximum amount by which the completion time of the entire
job can be shortened? ' T T2 T3
6) ————> @ mm? 6)
T4 T5 T6 A) It cannot be reduced.
B) 1 minute C) 2 minutes D) 3 minutes Page 6 19. 20. 21. 22. Suppose a pizza delivery person needs to take pizzas to 10 houses in different
neighborhoods and then return to pick up the next set to be delivered. The technique
most likely to be useful in solving this problem is  A) ﬁnding an Euler circuit on a graph. B) applying the nearest—neighbor algorithm for the traveling salesman problem. C) applying Kruskal's algorithm for ﬁnding a minimum—cost spanning tree for a graph
D) None of these techniques is likely to apply. A local cafeteria offers a choice of 5 meats, 6 vegetables, and 3 salads. A complete
dinner includes 1 meat, 1 vegetable, and 1 salad How many different dinners can be
created? A) 14 B) 45 C) 90 D) 120 Given the order—requirement digraph below (with time given in minutes) and the priority
list Ti, T2, T 3, T4, T5, T5, T7, apply the list—processing algorithm to construct a schedule
using two processors. How much time does the resulting schedule require? 6) @_______;@ ~—'———e®
:®/ \Ts® A) 16———% minutes
B) 17 minutes
C) 18 minutes
D) 21 minutes "E Use the decreasing—time—list algorithm to schedule these tasks on two machines:
3 minutes, 5 minutes, 8 minutes, 4 minutes, 6 minutes, 2 minutes How much time does the resulting schedule require? A) 14 minutes B) 15 minutes C) 16 minutes D) 18 minutes Page 7 23 .' What is the minimum time required to complete eight independent tasks on two
processors when the sum of all the times of the eight tasks is 72 minutes?
A) 4 minutes
B) 9 minutes
C) 16 minutes
D) 36 minutes 24. Choose the packing that results from the use of the ﬁrst ﬁt (FF) binpacking algorithm to
pack the following weights into bins that can hold no more than 8 lbs.
6 lbs, 2 lbs, 4 lbs, 3 lbs, 5 lbs, 3 lbs, 2 lbs, 4 lbs “Ill "IHI
I “a
"IE IE" 25. Choose the packing that results from the use of the next ﬁt (N F) binpacking algorithm
to pack the following weights into bins that can hold no more than 8 lbs.
6 lbs, 2 lbs, 4 lbs, 3 lbs, 5 lbs, 3 lbs, 2 lbs, 4 lbs El It"
"a la
Ill Ell _ Page 8 26. Which of the following is a correct vertex coloring of the given graph? (Capital letters
indicate which color the vertex is colored.) LIN v R ILW a w. w 1r w a v v'
A) Ionly '
B) 11 only
C) v Bothland 11
D) Neitherln‘or II 27. Find the chromatic number of the graph below: ‘1’!
A! Page 9 ...
View
Full Document
 Fall '07
 Meyer

Click to edit the document details