Speedrunning is a popular activity in which the goal is to finish a video game as fast as possible. Players around the world spend hours each day on live stream, perfecting their skills to achieve a world record in well-known games such as Super Mario Bros, Castlevania or Mega Man. But human execution is not the only factor in a successful speed run. Some common techniques such as damage boosting or routing require careful planning to optimize time gains. In this paper, we show that optimizing

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... hese mechanics is in fact a profound algorithmic problem, as they lead to novel generalizations of the well-known NP-hard knapsack and feedback arc set problems. We show that the problem of finding the optimal damage boosting locations in a game admits an FPTAS and is FPT in k + r, the number k of enemy types in the game and r the number of health refill locations. However, if the player is allowed to lose a life to regain health, the problem becomes hard to approximate within a factor 1/2 but admits a (1/2 − )-approximation with two lives. Damage boosting can also be solved in pseudo-polynomial time. As for routing, we show various hardness results, including W [2]-hardness in the time lost in a game, even on bounded treewidth stage graphs. On the positive side, we exhibit an FPT algorithm for stage graphs of bounded treewidth and bounded in-degree. ACM Subject Classification Theory of computation → Design and analysis of algorithms, Theory of computation → Approximation algorithms analysis, Theory of computation → Parameterized complexity and exact algorithms Keywords and phrases Approximation algorithms, parameterized complexity, video games, knapsack, feedback arc set Digital Object Identifier 10.4230/LIPIcs.FUN.2018.27 1 The author acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for the financial support of this project. 2 All products, company names, brand names, trademarks, and sprites are properties of their respective owners. Video game screen-shots and sprites are used here under Fair Use for educational purposes.