6 research outputs found
Push-Pull Block Puzzles are Hard
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 recreational motion planning problem, similar to Sokoban, that involve
moving a `robot' on a square grid with obstacles. The obstacles
cannot be traversed by the robot, but some can be pushed and pulled by the
robot into adjacent squares. Thin walls prevent movement between two adjacent
squares. This work follows in a long line of algorithms and complexity work on
similar problems. The 2D push-pull block puzzle shows up in the video games
Pukoban as well as The Legend of Zelda: A Link to the Past, giving another
proof of hardness for the latter. This variant of block-pushing puzzles is of
particular interest because of its connections to reversibility, since any
action (e.g., push or pull) can be inverted by another valid action (e.g., pull
or push).Comment: Full version of CIAC 2017 paper. 17 page
Extremal Reaches in Polynomial Time
Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolutejointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm. Copyright 2011 ACM
Extremal Reaches in Polynomial Time
Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolutejointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm. Copyright 2011 ACM
Visualizing three-dimensional graph drawings
viii, 110 leaves : ill. (some col.) ; 29 cm.The GLuskap system for interactive three-dimensional graph drawing applies techniques of
scientific visualization and interactive systems to the construction, display, and analysis of
graph drawings. Important features of the system include support for large-screen stereographic
3D display with immersive head-tracking and motion-tracked interactive 3D wand
control. A distributed rendering architecture contributes to the portability of the system,
with user control performed on a laptop computer without specialized graphics hardware.
An interface for implementing graph drawing layout and analysis algorithms in the Python
programming language is also provided. This thesis describes comprehensively the work
on the system by the author—this work includes the design and implementation of the major
features described above. Further directions for continued development and research in
cognitive tools for graph drawing research are also suggested
Games, puzzles, and computation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 147-153).There is a fundamental connection between the notions of game and of computation. At its most basic level, this is implied by any game complexity result, but the connection is deeper than this. One example is the concept of alternating nondeterminism, which is intimately connected with two-player games. In the first half of this thesis, I develop the idea of game as computation to a greater degree than has been done previously. I present a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games. A deterministic version of Constraint Logic corresponds to a novel kind of logic circuit which is monotone and reversible. At the other end of the spectrum, I show that a multiplayer version of Constraint Logic is undecidable. That there are undecidable games using finite physical resources is philosophically important, and raises issues related to the Church-Turing thesis. In the second half of this thesis, I apply the Constraint Logic formalism to many actual games and puzzles, providing new hardness proofs. These applications include sliding-block puzzles, sliding-coin puzzles, plank puzzles, hinged polygon dissections, Amazons, Kohane, Cross Purposes, Tip over, and others.(cont.) Some of these have been well-known open problems for some time. For other games, including Minesweeper, the Warehouseman's Problem, Sokoban, and Rush Hour, I either strengthen existing results, or provide new, simpler hardness proofs than the original proofs.by Robert Aubrey Hearn.Ph.D