The steady development of motor vehicle technology will enable cars of the near future to assume an ever increasing role in the decision making and control of the vehicle itself. In the foreseeable future, cars will have the ability to communicate with one another in order to better coordinate their motion. This motivates a number of interesting algorithmic… (More)
In this project we consider the complexity of a particular class of puzzles, which we call 'slide and merge' games. The goal of such games is to produce a tile of a target value, by sliding and merging equal valued tiles. We review related work on similar games and one recent claim regarding a particularly popular game.
We study the computational complexity of a variant of the popular 2048 game in which no new tiles are generated after each move. As usual, instances are defined on rectangular boards of arbitrary size. We consider the natural decision problems of achieving a given constant tile value, score or number of moves. We also consider approximating the maximum… (More)
2048 is a single-player online puzzle game that went viral in March 2014. The game is played on a 4 × 4 board by sliding around and merging equal valued tiles to create tiles of higher value. The player wins by creating the 2048 valued tile, hence the name. We study the complexity of a slightly adapted version and prove that a number of natural decision… (More)
The most important NP-Complete (logic) problem family!
We study complex non-zero-sum iterated two player games, more specifically, various strategies and their performances in iterated travelerâÂ Â s dilemma (ITD). We focus on the relative performances of several types of parameterized strategies, where each such strategy type corresponds to a particular âÂ Â philosophyâÂ Â on how to best… (More)