Minimum Consistent Subset in Interval Graphs and Circle Graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910457814581248 |
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| author | Manna, Bubai |
| author_facet | Manna, Bubai |
| contents | In a connected simple graph G = (V,E), each vertex of V is colored by a color from the set of colors C={c1, c2,..., c_α}$. We take a subset S of V, such that for every vertex v in V§, at least one vertex of the same color is present in its set of nearest neighbors in S. We refer to such a S as a consistent subset. The Minimum Consistent Subset (MCS) problem is the computation of a consistent subset of the minimum size. It is established that MCS is NP-complete for general graphs, including planar graphs. We expand our study to interval graphs and circle graphs in an attempt to gain a complete understanding of the computational complexity of the \mcs problem across various graph classes.
This work introduces an (4α+ 2)- approximation algorithm for MCS in interval graphs where αis the number of colors in the interval graphs. Later, we show that in circle graphs, MCS is APX-hard. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum Consistent Subset in Interval Graphs and Circle Graphs Manna, Bubai Computational Geometry In a connected simple graph G = (V,E), each vertex of V is colored by a color from the set of colors C={c1, c2,..., c_α}$. We take a subset S of V, such that for every vertex v in V§, at least one vertex of the same color is present in its set of nearest neighbors in S. We refer to such a S as a consistent subset. The Minimum Consistent Subset (MCS) problem is the computation of a consistent subset of the minimum size. It is established that MCS is NP-complete for general graphs, including planar graphs. We expand our study to interval graphs and circle graphs in an attempt to gain a complete understanding of the computational complexity of the \mcs problem across various graph classes. This work introduces an (4α+ 2)- approximation algorithm for MCS in interval graphs where αis the number of colors in the interval graphs. Later, we show that in circle graphs, MCS is APX-hard. |
| title | Minimum Consistent Subset in Interval Graphs and Circle Graphs |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2405.14493 |