
RedBlue Point Separation for Points on a Circle
Given a set R of red points and a set B of blue points in the plane, the...
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Optimal Discretization is Fixedparameter Tractable
Given two disjoint sets W_1 and W_2 of points in the plane, the Optimal ...
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Exact Method for Generating StrategySolvable Sudoku Clues
A Sudoku puzzle often has a regular pattern in the arrangement of initia...
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Searching for Point Locations using Lines
Versions of the following problem appear in several topics such as Gamma...
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Separating Geometric Data with Minimum Cost: Two Disjoint Convex Hulls
In this study, a geometric version of an NPhard problem ("Almost 2SAT"...
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Quantum algorithms for computational geometry problems
We study quantum algorithms for problems in computational geometry, such...
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The shortest way to visit all metro lines in Paris
What if {a tourist, a train addict, Dr. Sheldon Cooper, somebody who lik...
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On the Parameterized Complexity of RedBlue Points Separation
We study the following geometric separation problem: Given a set R of red points and a set B of blue points in the plane, find a minimumsize set of lines that separate R from B. We show that, in its full generality, parameterized by the number of lines k in the solution, the problem is unlikely to be solvable significantly faster than the bruteforce n^O(k)time algorithm, where n is the total number of points. Indeed, we show that an algorithm running in time f(k)n^o(k/ k), for any computable function f, would disprove ETH. Our reduction crucially relies on selecting lines from a set with a large number of different slopes (i.e., this number is not a function of k). Conjecturing that the problem variant where the lines are required to be axisparallel is FPT in the number of lines, we show the following preliminary result. Separating R from B with a minimumsize set of axisparallel lines is FPT in the size of either set, and can be solved in time O^*(9^B) (assuming that B is the smallest set).
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