DeepAI AI Chat
Log In Sign Up

On the NP-Completeness of Satisfying Certain Path and Loop Puzzles

by   Hadyn Tang, et al.

"Eye-Witless", "Haisu" and "Oriental House" are genres of logic puzzles invented by William Hu, and "Detour" is a genre of logic puzzle invented by online user Guowen Zhang. Each of these puzzles revolves around constructing a path or loop through the cells of a grid according to certain constraints given by clues in the grid. We prove that deciding whether a particular puzzle in each of these genres is solvable is NP-complete.


page 3

page 10

page 13

page 14


A Framework for Loop and Path Puzzle Satisfiability NP-Hardness Results

Building on the results published in arxiv:2004.12849 we present a gener...

ZHED is NP-complete

We prove that the 2017 puzzle game ZHED is NP-complete, even with just 1...

Hamiltonicity is Hard in Thin or Polygonal Grid Graphs, but Easy in Thin Polygonal Grid Graphs

In 2007, Arkin et al. initiated a systematic study of the complexity of ...

A Complexity Dichotomy for Permutation Pattern Matching on Grid Classes

Permutation Pattern Matching (PPM) is the problem of deciding for a give...

Path Puzzles: Discrete Tomography with a Path Constraint is Hard

We prove that path puzzles with complete row and column information--or ...

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible

We analyze the computational complexity of the many types of pencil-and-...

NP Decision Procedure for Monomial and Linear Integer Constraints

Motivated by satisfiability of constraints with function symbols, we con...