Abstract
Consider an agent traversing a graph of “gadgets”, each with local state that changes with each traversal by the agent. Prior work has studied the computational complexity of deciding whether the agent can reach a target location given a graph containing many copies of a given type of gadget. This paper introduces new goals and studies examples where the computational complexity of these problems are the same or differ from the original relocation goal. For several classes of gadgets—DAG gadgets, one-state gadgets, and reversible deterministic gadgets—we give a partial characterization of their complexity when the goal is to traverse every gadget at least once. We also study the complexity of reconfiguration, where the goal is to bring the entire system of gadgets to a specified state. We give examples where reconfiguration is a strictly harder problem than relocating the agent, and also examples where relocation is strictly harder. We also give a partial characterization of the complexity of reconfiguration with reversible deterministic gadgets.
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Notes
- 1.
Assembly and motion planning literature often use the term reachability to refer to whether an agent can reach a target location. However, reconfiguration literature uses the term to refer to whether a target location in the configuration space is reachable from another. This would be equivalent to our reconfiguration problem which also specifies a target location for the agent.
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Acknowledgments
This work grew out of an open problem session and a final project from MIT class on Algorithmic Lower Bounds: Fun with Hardness Proofs (6.892) from Spring 2019.
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Ani, J., Demaine, E.D., Diomidov, Y., Hendrickson, D., Lynch, J. (2022). Traversability, Reconfiguration, and Reachability in the Gadget Framework. In: Mutzel, P., Rahman, M.S., Slamin (eds) WALCOM: Algorithms and Computation. WALCOM 2022. Lecture Notes in Computer Science(), vol 13174. Springer, Cham. https://doi.org/10.1007/978-3-030-96731-4_5
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DOI: https://doi.org/10.1007/978-3-030-96731-4_5
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