Published on January 11, 2014
Interesting Problems in Computer Science Part – I (Probability) Harsh Hemani BARC
Monty Hall Problem Subject Area: Probability Theory Suppose that you're on a game show. You are asked to choose one out of three doors. Behind one door is a car; behind others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?“ Is it to your advantage to switch your choice?
Multi-armed Bandit Problem Subject Area: Probability Theory In the multi-arm bandit problem, the gambler has to decide which arm of K different slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff). Challenge lies in devising a strategy to maximize the profit in minimum trials.
Group Russian Roulette Subject Area: Probability Theory A room has N angry people. At each chime of the clock, everyone in the room simultaneously spins around and shoots a random other person. The persons shot fall dead. The survivors spin and shoot again at the next chime. Eventually, either all are dead or there is a survivor. As N grows, what is the limiting probability that there will be a survivor?
Chomp Subject Area: Probability Theory Cookies are set out on a 2 dimensional grid. The bottom left cookies is poisoned. Two players take turns to eat (chomp) the cookies, eating one of the remaining cookies plus all the above and to the right of that cookie. The looser is the player who has to eat the poisoned cookie. The question is, does a winning strategy exist? What happens in a 3D or a 4D grid?
Empires and Percolation Subject Area: Probability Theory Consider a partition of a plane into polygonal sets, which we call empires. Two empires are adjacent if they share a non-trivial boundary line. We consider a process whose only qualitative dynamics is that two adjacent empires can merge. Any two adjacent empires can merge at stochastic rate r, which depends on the geometry of the two empires. We are interested in knowing the conditions on stochastic rate r which are sufficient for percolation.
Next part: Graph Theory Disclaimer: Author claims non of the problems as of his own. Problems have been collected from various sources. The are presented here to motivate people in computer science and mathematics
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