On the computational complexity of portal and push-pull block puzzles
Name
965798956-MIT.pdf
Description
Full printable version
Size
1.23 MB
Format
Adobe PDF
Checksum (MD5)
ea040a57f7992255db6b1af8bbe8eda1
Author(s)
Lynch, Jayson (Jayson R.)
Advisor(s)
Erik Demaine.
Date Issued
2015
Publisher
Massachusetts Institute of Technology
Abstract
We classify the computational complexity of two types of motion planning problems represented in games. Portal, a popular video game, is shown to be NP-hard or PSPACE-complete depending on the game mechanics allowed. Push-pull block puzzles are games, similar to Sokoban, which involve moving a 'robot' on a square grid with obstacles and blocks that can be pushed or pulled by the robot into adjacent squares. We prove that push-pull block puzzles in 3D and push-pull block puzzles in 2D with thin walls are NP-hard to solve. We also show certain 3D push-pull block puzzles are PSPACE-complete. This work follows in a long line of algorithms and complexity work on similar problems Wil91, DDO00, Hof00, DHH04, DH01, DO92, DHH02, Cul98, DZ96, Rit10]. The 2D push-pull block puzzle also shows up in a number of video games, thus implying other results, further continuing the work on understanding video games as in Vig12, ADGV14, For10, Cor04.
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 49-53).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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