 Hello everyone, this is Alice Gao. In this video, I'm going to describe several applications of search algorithms. Let me talk about a class of problems called propositional satisfiability. We have a propositional formula with several variables. Is it possible to assign true or false to each variable so that the formula is true? This is an example of a broad class of problems called satisfiability or SAT problems. One application of this problem is the FCC spectrum auction. The purpose of the FCC spectrum auction is to buy back radio spectrums from TV broadcasters and sell them to the telecom companies, the companies who provide services for our phones. When the FCC is buying back the radio spectrums, they will offer a price to the TV broadcasters. Depending on the price, some TV broadcasters will be willing to give up their spectrums and go off air. Other TV broadcasters may decide to hold on to their spectrums and stay on air. For the TV broadcasters who decide to remain on air, FCC may need to reassign as spectrums so that the companies do not interfere with one another. This is a packing problem and it can be formulated as a propositional satisfiability problem. This slide has an extremely small problem and it is easy to solve. For the FCC spectrum auction, solving the packing problem is computationally challenging. First, the formulas are huge and have a lot of variables in them. Second, we need to solve a huge number of such problems. Finally, we need to solve each problem instance very quickly, perhaps up to a minute per problem. My postdoc advisor Kevin Layton-Brown and his students worked on developing efficient algorithms to solve this problem. If you are interested, check out the news article and some papers related to this project. This is a classic Chinese lighting puzzle called Huayun Dao. I got a copy of this puzzle when I was a child. I couldn't solve the puzzle for a long time. Don't worry if you don't understand the Chinese characters. You don't need to understand Chinese to enjoy this puzzle. Let me tell you about the story behind this puzzle. In the romance of the Three Kingdoms, there was a famous battle called the Battle of the Red Cliffs, between the Wei Kingdom and the Shu Kingdom. The Wei Kingdom is led by their general called Cao Cao. The Shu Kingdom has a famous strategist called Zhu Ge Liang. Cao Cao was badly defeated and he fled with a handful of soldiers. The only way for Cao Cao to escape alive was through the narrow Huayun Dao or Huayun Pass. Zhu Ge Liang anticipated this and placed his best generals at Huayun Dao. These generals are Zhang Fei, Ma Chao, Zhao Yun, Huang Zhong and Guan Yu. Cao Cao was an amazing warrior and he defeated the first four generals. When he saw Guan Yu, Cao Cao felt a sense of despair. Guan Yu was the best and Cao Cao knew that he had no hope of defeating Guan Yu. Luckily for Cao Cao, the two knew each other before. Guan Yu was once a guest at Cao Cao's place and Cao Cao showed him considerable kindness. By appealing to their friendship, Cao Cao persuaded Guan Yu to let him escape. This was the story of Huayun Dao. This puzzle shows Cao Cao trying to escape through Huayun Dao and the other people trying to stop him. Our goal is to slide the pieces horizontally or vertically until Cao Cao escapes from the bottom opening. In other words, we want to move Cao Cao to this 2x2 region. The puzzle has many other initial configurations. You can check out other initial configurations on the Chinese Wikipedia page. Next, let me talk about a few simple and stylized problems. The eight puzzle is a sliding puzzle. The numbers 1 to 8 are in a 3x3 grid. Our goal is to move the tiles horizontally or vertically until we transform the puzzle to the goal position. The next one is a river crossing problem called the wolf, goat and cabbage problem. Here's a description from Wikipedia. Once upon a time, a farmer went to a market and purchased a wolf, a goat and a cabbage. On their way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only themselves and the single one of their purchases. The wolf, the goat or the cabbage. If left unattended together, the wolf would eat the goat or the goat would eat the cabbage. The farmer's challenge was to carry themselves and the purchases to the far bank of the river, leaving each purchase intact. How did the farmer do it? This is the N Queens problem. We have an 8x8 chess board. We want to put eight queens on the board such that no two queens attack each other. A queen attacks anything in the same row in the same column and in the same diagonal. This is also a classic constraint satisfaction problem. That's everything on applications of search problems. If you came across other interesting applications, please let me know. Thank you very much for watching. I will see you in the next video. Bye for now.