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Related papers: Pushing Blocks without Fixed Walls via Checkable G…

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We prove PSPACE-completeness of the well-studied pushing-block puzzle Push-1F, a theoretical abstraction of many video games (introduced in 1999). The proof also extends to Push-$k$ for any $k \ge 2$. We also prove PSPACE-completeness of…

Computational Complexity · Computer Science 2024-12-31 Hayashi Ani , Lily Chung , Erik D. Demaine , Jenny Diomidova , Della Hendrickson , Jayson Lynch

Push-1 is one of the simplest abstract frameworks for motion planning; however, the complexity of deciding if a Push-1 problem can be solved was a several-decade-old open question. We resolve the complexity of the motion planning problem…

Computational Complexity · Computer Science 2025-09-03 Zachary DeStefano , Bufang Liang

Consider $n^2-1$ unit-square blocks in an $n \times n$ square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable -- a variation of Rush Hour with only $1 \times 1$ cars and fixed…

Computational Complexity · Computer Science 2020-05-05 Josh Brunner , Lily Chung , Erik D. Demaine , Dylan Hendrickson , Adam Hesterberg , Adam Suhl , Avi Zeff

We prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of…

Computational Complexity · Computer Science 2023-11-16 Hayashi Ani , Sualeh Asif , Erik D. Demaine , Jenny Diomidova , Dylan Hendrickson , Jayson Lynch , Sarah Scheffler , Adam Suhl

We prove that two pushing-blocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a…

Computational Geometry · Computer Science 2007-05-23 Erik D. Demaine , Martin L. Demaine , Joseph O'Rourke

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of…

Computational Complexity · Computer Science 2017-09-06 Erik D. Demaine , Isaac Grosof , Jayson Lynch

We investigate the reconfiguration of $n$ blocks, or "tokens", in the square grid using "line pushes". A line push is performed from one of the four cardinal directions and pushes all tokens that are maximum in that direction to the…

Combinatorics · Mathematics 2023-10-16 Hugo A. Akitaya , Maarten Löffler , Giovanni Viglietta

We prove PSPACE-completeness of several reversible, fully deterministic systems. At the core, we develop a framework for such proofs (building on a result of Tsukiji and Hagiwara and a framework for motion planning through gadgets), showing…

Computational Complexity · Computer Science 2022-07-18 Erik D. Demaine , Robert A. Hearn , Dylan Hendrickson , Jayson Lynch

We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game *PushPush*, consists of unit square blocks on an integer…

Computational Geometry · Computer Science 2007-05-23 Erik D. Demaine , Martin L. Demaine , Joseph O'Rourke

We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse…

Computational Complexity · Computer Science 2007-05-23 Robert A. Hearn , Erik D. Demaine

An open-close door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "opening" and "closing" tunnels set the gadget's state to open and closed, respectively, while the "traverse" tunnel can…

Computational Complexity · Computer Science 2026-03-17 MIT Gadgets Group , Jeffrey Bosboom , Erik D. Demaine , Jenny Diomidova , Dylan Hendrickson , Hayashi Layers , Jayson Lynch

The pebble-motion on graphs is a subcategory of multi-agent pathfinding problems dealing with moving multiple pebble-like objects from a node to a node in a graph with a constraint that only one pebble can occupy one node at a given time.…

Robotics · Computer Science 2020-07-21 Miroslav Kulich , Tomáš Novák , Libor Přeucil

We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move…

Computational Geometry · Computer Science 2007-05-23 Joseph O'Rourke , The Smith Problem Solving Group

We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position,…

Computational Complexity · Computer Science 2018-03-13 Jeffrey Bosboom , Erik D. Demaine , Mikhail Rudoy

In this work, we introduce a framework that enables highly maneuverable locomotion using non-periodic contacts. This task is challenging for traditional optimization and planning methods to handle due to difficulties in specifying contact…

Robotics · Computer Science 2024-11-05 Xiaohan Liu , Cunxi Dai , John Z. Zhang , Arun Bishop , Zachary Manchester , Ralph Hollis

We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…

Computational Complexity · Computer Science 2018-06-13 Erik D. Demaine , Isaac Grosof , Jayson Lynch , Mikhail Rudoy

This paper addresses the problem of pushing manipulation with nonholonomic mobile robots. Pushing is a fundamental skill that enables robots to move unwieldy objects that cannot be grasped. We propose a stable pushing method that maintains…

Robotics · Computer Science 2023-09-26 Yujie Tang , Hai Zhu , Susan Potters , Martijn Wisse , Wei Pan

We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around…

We study two well-known reconfiguration problems. Given a start and a target configuration of geometric objects in a polygon, we wonder whether we can move the objects from the start configuration to the target configuration while avoiding…

Computational Geometry · Computer Science 2024-12-31 Mikkel Abrahamsen , Kevin Buchin , Maike Buchin , Linda Kleist , Maarten Löffler , Lena Schlipf , André Schulz , Jack Stade

This work explores the use of topological tools for achieving effective non-prehensile manipulation in cluttered, constrained workspaces. In particular, it proposes the use of persistent homology as a guiding principle in identifying the…

Robotics · Computer Science 2022-02-08 Ewerton R. Vieira , Daniel Nakhimovich , Kai Gao , Rui Wang , Jingjin Yu , Kostas E. Bekris
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