On the parameterized complexity of the generalized rush hour puzzle
نویسندگان
چکیده
We consider the parameterized complexity of a generalized version of the game Rush Hour , which is a puzzle requiring the player to find a sequence of moves by vehicles to enable a special target vehicle to escape from a grid-shaped game board that may contain obstacles. Although the problem is PSPACE-complete, we demonstrate algorithms that work in polynomial time when either the total number of vehicles or the total number of moves is bounded by a constant. Our contributions are two-fold, entailing the application of ideas of parameterized complexity to games and to motion-planning problems (albeit motion-planning problems of a very constrained nature).
منابع مشابه
A Structural Complexity Measure for Predicting Human Planning Performance
Humans have an impressive ability to solve even computationally complex problems. Limited cognitive processing capabilities, however, impede an exhaustive search of the problem space. Thus, planning problems of the same size may require a different cognitive effort. Formal complexity aspects are inherent to a problem and set computational limits that a solver must deal with. For a measure of co...
متن کاملLimits of Rush Hour Logic Complexity
Rush Hour Logic was introduced in [2] as a model of computation inspired by the \Rush Hour" toy puzzle, in which cars can move horizontally or vertically within a parking lot. The authors show how the model supports polynomial space computation, using certain car con gurations as building blocks to construct boolean circuits for a cpu and memory. They consider the use of cars of length 3 crucia...
متن کاملRush Hour is PSPACE-complete
In this report we give a formal definition of the sliding block puzzle Rush Hour and we report on the proof showing that Rush Hour is PSPACE-complete from “The nondeterministic constraint logic model of computation: Reductions and applications” by Hearn and Demaine (Proceedings ICALP 2002).
متن کاملParameterized Complexity of Graph Constraint Logic
Graph constraint logic is a framework introduced by Hearn and Demaine [6], which provides several problems that are often a convenient starting point for reductions. We study the parameterized complexity of Constraint Graph Satisfiability and both bounded and unbounded versions of Nondeterministic Constraint Logic (NCL) with respect to solution length, treewidth and maximum degree of the underl...
متن کاملPSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation
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 the direction of a particular edge is shown to be PSPACEcomplete by a reduction from Quantified Boolean Formulas. We prove this result in a variety of specia...
متن کامل