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.

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 team’s 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

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.

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 lion’s 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)?

The shipping problem cont’d 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.

The shipping problem cont’d 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? (don’t 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?

The shipping problem cont’d 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?

The shipping problem cont’d 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 one that minimizes empty space)? Is the best packing achieved in larger or smaller boxes?

The shipping problem cont’d Strategy: divide and conquer. Complex problem divided into simpler parts. The problem-solving group may break down into two parts now.

The shipping problem cont’d Problem I: Do we need large boxes or small boxes? Box sides that touch each other are “wasted”, so need fewest touching sides, that is largest boxes within the other given constraints.

The shipping problem cont’d Problem II: Spheres packed inside the box. What box size will optimize the packing, that is minimize the “wasted” empty space? Heuristic: simplify.

The shipping problem cont’d Problem II: Spheres packed inside the box. What box size will optimize the packing, that is minimize the “wasted” empty space? Heuristic: simplify. 1.3D -> 2D (circles in a square) 2.Get a feel for it. One circle.

The shipping problem cont’d Problem II: Spheres packed inside the box. Heuristic: circles in a sphere. Maximize packing density = (volume of spheres)/(volume of box) Now back to the spheres:

The shipping problem cont’d 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 = k^2 We want the box size so that integer # balls of 2,3,5 (diameters 4,6,10) fit. a=60*m. Thus, 60*m = k^2. 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 >> ball size the surface/volume arguments suggest that we can achieve a close to optimal packing even without being perfect.

The shipping problem cont’d Our tactical steps (heurtsics ) from the beginning: 1.Brainstorm 2.Divide and Conquer 3.Simplify 4.Get hands dirty. Explore trends.

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?

Combinatorics cont’d Problem: “Random Play” on your I-Touch works like this. When pressed once, it plays a random song from your library of N >> 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 << N). What are the chances you will hear your one most favorite song?

Combinatorics Cont’d 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”.