Dots Polygons

04/02/2020
by   Kevin Buchin, et al.
0

We present a new game, Dots Polygons, played on a planar point set. Players take turns connecting two points, and when a player closes a (simple) polygon, the player scores its area. We show that deciding whether the game can be won from a given state, is NP-hard. We do so by a reduction from vertex-disjoint cycle packing in cubic planar graphs, including a self-contained reduction from planar 3-Satisfiability to this cycle-packing problem. This also provides a simple proof of the NP-hardness of the related game Dots Boxes. For points in convex position, we discuss a greedy strategy for Dots Polygons.

READ FULL TEXT
research
02/21/2022

NP-Hardness of a 2D, a 2.5D, and a 3D Puzzle Game

In this paper, we give simple NP-hardness reductions for three popular v...
research
11/05/2019

Packing Trees into 1-planar Graphs

We introduce and study the 1-planar packing problem: Given k graphs with...
research
02/19/2018

(Arc-disjoint) cycle packing in tournament: classical and parameterized complexity

Given a tournament T, the problem MaxCT consists of finding a maximum (a...
research
06/19/2022

The Game of Tumbleweed is PSPACE-complete

Tumbleweed is a popular two-player perfect-information new territorial g...
research
10/09/2017

Two-player entangled games are NP-hard

We show that the maximum success probability of players sharing quantum ...
research
03/30/2022

Wordle is NP-hard

Wordle is a single-player word-guessing game where the goal is to discov...
research
02/04/2012

e-Valuate: A Two-player Game on Arithmetic Expressions -- An Update

e-Valuate is a game on arithmetic expressions. The players have contrast...

Please sign up or login with your details

Forgot password? Click here to reset