Toward a general complexity theory of motion planning: Characterizing which gadgets make games hard
Name
LIPIcs-ITCS-2020-62.pdf
Description
Published version
Size
1.39 MB
Format
Adobe PDF
Checksum (MD5)
c903a0882d37f7b4f3a00e977110c175
Author(s)
Demaine, Erik D
Hendrickson, Dylan H.
Lynch, Jayson R.
Date Issued
January 2020
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Citation
Demaine, Erik D., Dylan H. Hendrickson and Jayson Lynch. “Toward a general complexity theory of motion planning: Characterizing which gadgets make games hard.” Leibniz International Proceedings in Informatics, LIPIcs, 151, 1 (January 2020): 1-42 © 2020 The Author(s)
Version
Final published version
Abstract
We begin a general theory for characterizing the computational complexity of motion planning of robot(s) through a graph of “gadgets”, where each gadget has its own state defining a set of allowed traversals which in turn modify the gadget’s state. We study two general families of such gadgets within this theory, one which naturally leads to motion planning problems with polynomially bounded solutions, and another which leads to polynomially unbounded (potentially exponential) solutions. We also study a range of competitive game-theoretic scenarios, from one player controlling one robot to teams of players each controlling their own robot and racing to achieve their team’s goal. Under certain restrictions on these gadgets, we fully characterize the complexity of bounded 1-player motion planning (NL vs. NP-complete), unbounded 1-player motion planning (NL vs. PSPACE-complete), and bounded 2-player motion planning (P vs. PSPACE-complete), and we partially characterize the complexity of unbounded 2-player motion planning (P vs. EXPTIME-complete), bounded 2-team motion planning (P vs. NEXPTIME-complete), and unbounded 2-team motion planning (P vs. undecidable). These results can be seen as an alternative to Constraint Logic (which has already proved useful as a basis for hardness reductions), providing a wide variety of agent-based gadgets, any one of which suffices to prove a problem hard.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution 3.0 unported license
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DOI of Published Version
https://doi.org/10.4230/LIPIcs.ITCS.2020.62
