Traversability, Reconfiguration, and Reachability in the Gadget Framework
-
Published:2023-07-05
Issue:11
Volume:85
Page:3453-3486
-
ISSN:0178-4617
-
Container-title:Algorithmica
-
language:en
-
Short-container-title:Algorithmica
Author:
Ani Joshua, Demaine Erik D., Diomidov Yevhenii, Hendrickson Dylan, Lynch JaysonORCID
Abstract
AbstractConsider an agent traversing a graph of “gadgets”, where each gadget has local state that changes with each traversal by the agent according to specified rules. Prior work has studied the computational complexity of deciding whether the agent can reach a specified location, a problem we call reachability. This paper introduces new goals for the agent, aiming to characterize when the computational complexity of these problems is the same or differs from that of reachability. First we characterize the complexity of universal traversal—where the goal is to traverse every gadget at least once—for DAG gadgets (partially), one-state gadgets, and reversible deterministic gadgets. Then we study the complexity of reconfiguration—where the goal is to bring the system of gadgets to a specified state. We prove many cases PSPACE-complete, and show in some cases that reconfiguration is strictly harder than reachability, while in other cases, reachability is strictly harder than reconfiguration.
Funder
Massachusetts Institute of Technology
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,General Computer Science
Reference19 articles.
1. Akitaya, H.A., Demaine, E.D., Gonczi, A., Hendrickson, D.H., Hesterberg, A., Korman, M., Korten, O., Lynch, J., Parada, I., Sacristán, V.: Characterizing universal reconfigurability of modular pivoting robots. In: 37th International Symposium on Computational Geometry (2021) 2. Ani, J., Bosboom, J., Demaine, E.D., Diomidov, Y., Hendrickson, D., Lynch J.: Walking through doors is hard, even without staircases: proving PSPACE-hardness via planar assemblies of door gadgets. In: Proceedings of the 10th International Conference on Fun with Algorithms (FUN 2020), pp 3:1–3:23 (2020) 3. Ani, J., Chung, L., Demaine, E.D., Diomidov, Y., Hendrickson, D., Lynch, J.: Pushing blocks via checkable gadgets: Pspace-completeness of push-1f and block/box dude. In: 11th International Conference on Fun with Algorithms (FUN 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2022) 4. Ani, J., Demaine, E.D., Diomidov, Y., Hendrickson, D.H., Lynch, J.: Traversability, reconfiguration, and reachability in the gadget framework. In: Mutzel, Petra, Rahman, M.d. Saidur, Slamin, (eds.), Proceedings of the 16th International Conference and Workshops on Algorithms and Computation (WALCOM 2022), volume 13174 of Lecture Notes in Computer Science, pp 47–58, Jember, Indonesia (2022) 5. Ani, J., Demaine, E.D., Hendrickson, D., Lynch, J.: Trains, games, and complexity: 0/1/2-player motion planning through input/output gadgets. In: Mutzel, Petra, Rahman, Md. Saidur, Slamin (eds.), Proceedings of the 16th International Conference and Workshops on Algorithms and Computation (WALCOM 2022), volume 13174 of Lecture Notes in Computer Science, pp 187–198, Jember, Indonesia, March 24–26 (2022)
|
|