How do we determine the fastest path to cover an area using an object of some radius r? E.g. a machine that needs to spray a chemical onto a surface. I assume this is some kind of NP-hard problem.
2026-03-27 07:12:11.1774595531
Fastest path to cover area
99 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in APPROXIMATION
- Does approximation usually exclude equality?
- Approximate spline equation with Wolfram Mathematica
- Solving Equation with Euler's Number
- Approximate derivative in midpoint rule error with notation of Big O
- An inequality involving $\int_0^{\frac{\pi}{2}}\sqrt{\sin x}\:dx $
- On the rate of convergence of the central limit theorem
- Is there any exponential function that can approximate $\frac{1}{x}$?
- Gamma distribution to normal approximation
- Product and Quotient Rule proof using linearisation
- Best approximation of a function out of a closed subset
Related Questions in NP-COMPLETE
- Divide set into two subsets of equal sum and maximum this sum
- Linear Programming Primal-Dual tough question
- Bipartite Graph Partitioning (special case)
- Minimise the sum of pairwise distances between labelled points in a metric space subject to covering some set of labels
- How should a chain of proof be written?
- Show the NP completeness of Hamiltonian Path with the knowledge of an directed Euler graph
- Integer Programming (non $0-1$) Reduction to show $NP$ Completeness
- Categories with at most one arrow between any pair of objects. (appears in NPC)
- Find a generalized path cover of a square graph
- Generalize minimum path cover
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Seems to me that the total area painted is (roughly) the area of the brush times the length of the path. So, if two paths cover the same area, without overlaps, then they must have the same length. Time will be wasted if we have to lift the brush from the paper, though, so my argument only applies to continuous paths (with no lifts).
This kind of problem arises in many NC (numerical control) applications, and has been well studied. For example, trying to mill a region with an NC cutter is somewhat the same problem as painting. Here's one paper on the subject.