Multivariate Complexity Analysis of Geometric {\sc Red Blue Set Cover}
Pradeesha Ashok, Sudeshna Kolay, Saket Saurabh

TL;DR
This paper explores the parameterized complexity of a geometric variant of the Red Blue Set Cover problem, analyzing its tractability and kernelization properties based on various parameters.
Contribution
It provides a comprehensive complexity classification of Gen-RBSC-lines, including FPT algorithms, hardness results, and a kernelization dichotomy.
Findings
Gen-RBSC-lines is W-hard or FPT depending on parameters.
A nontrivial FPT algorithm exists for combined parameters $k_ ext{ell}$ and $k_r$.
Complete kernelization dichotomy established for the problem.
Abstract
We investigate the parameterized complexity of GENERALIZED RED BLUE SET COVER (Gen-RBSC), a generalization of the classic SET COVER problem and the more recently studied RED BLUE SET COVER problem. Given a universe containing blue elements and red elements, positive integers and , and a family of sets over , the \srbsc\ problem is to decide whether there is a subfamily of size at most that covers all blue elements, but at most of the red elements. This generalizes SET COVER and thus in full generality it is intractable in the parameterized setting. In this paper, we study a geometric version of this problem, called Gen-RBSC-lines, where the elements are points in the plane and sets are defined by lines. We study this problem for an array of parameters, namely, , and , and all possible…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · graph theory and CDMA systems
