Why are google maps displayed incorrectly?

What are some of the different algorithmically challenging problems with well defined solutions used in the companies like Facebook and Google?

• We learn a lot of Algorithms from textbooks and other sources. But a vast majority of problems encountered in real world that have well defined solutions are easily recognized. For example: Finding a shortest path from a source to destination in Google Maps would use a shortest path algorithm. It is evident that any programmer would easily figure out that it is a shortest path problem. Also he wont have trouble figuring out how the Graph should be constructed. And even if he did not know shortest path algorithm (this is not a very good example) he could refer a research paper and writing the code would be trivial. Lets take an example of non-real world problem. Suppose we have a chess board with some of the cells missing. What is the maximum number of rooks can we place in the chess board so that no rook is attacking another? This is a fairly difficult problem with well defined solution and can be solved by maximum bipartite matching. However even if one knew that this is a bipartite matching problem one would still need to figure out what should be the vertices and how to construct the graph. Many problems involving Dynamic Programming (DP) problems are difficult. Sometimes we use Dynamic Programming in trees and graphs. If the problem is not a very popular problem like LCS, RMQ, LCA, then we need to spend time thinking what should be the DP state. From my experience most of the problems in the industries which have a well defined solution are easy to notice. Moreover they come up as popular problems. Ofcourse there are mostly problems that don't have a well defined solutions, like what should be displayed in the News Feed of Facebook.  But that is not my concern. I want to know what are such problems that have well defined solutions and they are not easy to figure what algorithm is to be used. Also if algorithm were to be known it is not so easy to code it because the algorithm is not directly applicable or are not popular.

• Answer:

  Some problems that may appear in the industry. Airplane ticket pricing: Given a large set of historical pricing rules. Find out a set of legs for a trip that optimize for cost and travel time. Maps: Points of interest. Given a point on a map, find the closest k points of interest to this current point. Geo location. Given a point on a map, find the county the point is in. Pathfinding. The algorithms you learn in school won't work well on a graph that spans the entire US or the entire world, but there are great algorithms that tackle the problem. Web Search: Build an approximate autocomplete feature for a large dictionary (Google Suggest, Facebook/Quora autocomplete). Spell correction. Segmentation. Given a string of letters without spaces find a way to segment them into words. (it's a frequent problem in german, chinese, japanese or korean). Computing Pagerank. Computing the eigen vectors for a huge sparse matrix needs some interesting algebraic algorithms. Machine Translation. Spam detection. Ads: Ad Serving. Given many contracts that list different types of targeting and a user view. Evaluate fast which contracts are eligible to show an ad. Inventory Management. Selling reservation based targeted advertisements becomes an allocation problem that can be translated in a network flow problem. Infrastructure: Distributed hash tables for caching. Distributed sort for hadoop/mapreduce.