WADS 2013: Algorithms and Data Structures pp 328-340

# Approximation Algorithms for B1-EPG Graphs

• Dror Epstein
• Martin Charles Golumbic
• Gila Morgenstern
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

## 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 B1-EPG graphs. The motivation for studying these graphs comes from the context of circuit layout problems. It is known that recognizing B1-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 B1-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 B1-EPG graphs, even when the EPG representation is not given.

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## Authors and Affiliations

• Dror Epstein
• 1
• 2
• Martin Charles Golumbic
• 1
• 2
• Gila Morgenstern
• 2
1. 1.Department of Computer ScienceUniversity of HaifaIsrael
2. 2.Caesarea Rothschild Institute (CRI)University of HaifaIsrael