Principles of Teamwork

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Principles of Teamwork

• Learning how to function as a team member, and
  make your team succeed is one of the key
  objectives of this course. You can not get a good
  grade without it.
• Team work requires work. Not a free lunch. Pays
  off though.

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The indisputable laws of teamwork

• The Law of Significance. People try to achieve
  great things by themselves mainly because of the
  size of their ego, their level of insecurity, or
  simple naiveté and temperament.
• The Law of the Big Picture. The goal is more
  important than the role. Members must be willing
  to subordinate their roles and personal agendas
  to support the team vision.
• The Law of the Niche. All players have a place
  where they add the most value. Essentially, when
  the right team member is in the right place,
  everyone benefits.
• The Law of The Bad Apple. Rotten attitudes ruin
  a team. The first place to start is with
  yourself. Are you at our best?
• The Law of Countability. Teammates must be able
  to count on each other when it counts. Are you
  dedicated to the teams success? Can people
  depend on you?
• The Law of Communication. Interaction fuels
  action. Effective teams have teammates who are
  constantly talking, and listening to each other.
• The Law of Dividends. Investing in the team
  compounds over time. Make the decision to build a
  team

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Principles of Teamwork

• An important heuristic Set up regular meeting
  times, rather than planning ad-hoc meetings. At
  least once a week a back-up time. Tie to HW
  deadlines. You can not skip a meeting, unless
  the whole team decides it is not needed.

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Now, a real life problem.

• Group project preparation. Break out in groups.
  Each group will earn activity points for the
  in-class work.

SET-UP A sports equipment company manufactures
3 types of balls golf, ping-pong, and tennis.
The sizes (radii) of the balls are 2, 3, and 5
cm respectively. The company ships each ball type
separately, but uses only one size of container
for all its shipping needs. The container is a
perfect cube made out of padded, thermally
insulating material (nano-carbon trace
amounts of gold). The boxes are loaded on the
trucks by a single worker, using only her sheer
muscle power. A lions share of the shipping
cost in the cost of just getting the truck from
A to B, so sending trucks partially filled with
the merchandize is not optimal. PROBLEM What
is the optimal box size that will minimize the
shipping costs? How many balls of each type will
fit into such box (to within 10 relative
error)?
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The shipping problem contd

• Initial brainstorming

Boxes are expensive. Cost (cost per box) x(
number of boxes per truck). Each truck must be
filled with boxes, so we really need to minimize
cost per truck.
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The shipping problem contd
So it looks like we need to minimize the amount
of expensive carton used per box, while
preserving the total volume of all the boxes
that fill up the truck. Is this it? (dont
focus on the distilled problem yet!)
Strategy for complex problems Is this it? Is
this distilled problem the only one we need to
solve? Have we left anything out?
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The shipping problem contd
Remember, we need to maximize the amount of
merchandize (balls) per truck. Are we going to
have more of them in larger boxes or smaller
boxes? Second problem packing of hard
spheres. What is the best packing?
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The shipping problem contd
Remember, we need to maximize the amount of
merchandize (balls) per truck. Are we going to
have more of them in larger boxes or smaller
boxes? Second problem packing of hard
spheres. What is the best packing (that is the
onethat minimizes empty space)? Is the best
packing achieved in larger or smaller boxes?
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The shipping problem contd
Strategy divide and conquer. Complexproblem
divided into simpler parts. The problem-solving
group may break down into two parts now.
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The shipping problem contd
Problem I Do we need large boxesor small boxes?
Box sides that touch each other are wasted, so
need fewest touching sides, that is largest
boxes within the other given constraints.
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The shipping problem contd
Problem II Spheres packed inside the box. What
box size will optimize the packing, that is
minimize the wasted empty space? Heuristic
simplify.
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The shipping problem contd

• Problem II Spheres packed inside the
• box. What box size will optimize the packing,
  that is minimize
• the wasted empty space?
• Heuristic simplify.
• 3D -gt 2D (circles in a square)
• Get a feel for it. One circle.

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The shipping problem contd
Problem II Spheres packed inside the box.
Heuristic circles in a sphere. Maximize packing
density (volume of spheres)/(volume of
box) http//www.stetson.edu/efriedma/packing.htm
l Now back to the spheres http//en.wikipedia
.org/wiki/Sphere_packing
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The shipping problem contd

• What have we learned from the 2D case?

The dependence of the packing ratio on the box
size is not monotonic, but appears to reach an
asymptotic value of 0.78 for large size
box. Seems to occur at box size a k2 We want
the box size so that integer balls of 2,3,5
(diameters 4,6,10)fit. a60m. Thus, 60m k2.
Looks like this may lead to very large m, and
inadmissibly large box size. Need to Get away
from the exact packing. Fortunately, for large
box size a gtgt ball size the surface/volume
arguments suggest that we can achieve a close to
optimal packing even without being perfect.
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The shipping problem contd

• Our tactical steps (heurtsics ) from the
  beginning

1. Brainstorm
2. Divide and Conquer
3. Simplify
4. Get hands dirty. Explore trends.

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Combinatorics

• (Important to algorithm analysis )

Problem I How many N-bit strings contain at
least 1 zero? Problem II How many N-bit
strings contain more than 1 zero?
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Combinatorics contd
Problem Random Play on your I-Touch works
like this. When pressed once, it plays a random
song from your library of N gtgt 1 songs. When
pressed again, it excludes the song just played
from the library, and draws another song at
random from the remaining N-1 songs. Suppose you
have pressed Random Play k times (k ltlt N).
What are the chances you will hear your one
most favorite song?
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Combinatorics Contd
Problem DNA sequence contains only 4 letters
(A,T,G and C). Short words made of K
consecutive letters are the genetic code. Each
word (called codon, ) codes for a specific
amino-acid in proteins. There are a total of 20
biologically relevant amino-acids. Prove that
genetic code based on fixed K is degenerate,
that is there are amino-acids which are coded
for by more than one word.