Abstract
The edge intersection graphs of paths on a grid (or EPG graphs) are graphs whose vertices can be represented as simple paths on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. We consider the case of single-bend paths, namely, the class known as B 1-EPG graphs. The motivation for studying these graphs comes from the context of circuit layout problems. It is known that recognizing B 1-EPG graphs is NP-complete, nevertheless, optimization problems when given a set of paths in the grid are of considerable practical interest.
In this paper, we show that the coloring problem and the maximum independent set problem are both NP-complete for B 1-EPG graphs, even when the EPG representation is given. We then provide efficient 4-approximation algorithms for both of these problems, assuming the EPG representation is given. We conclude by noting that the maximum clique problem can be optimally solved in polynomial time for B 1-EPG graphs, even when the EPG representation is not given.
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Epstein, D., Golumbic, M.C., Morgenstern, G. (2013). Approximation Algorithms for B 1-EPG Graphs. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_29
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DOI: https://doi.org/10.1007/978-3-642-40104-6_29
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