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arXiv · 1106.3037

Efficient algorithm for the vertex connectivity of trapezoid graphs

Aleksandar Ilic
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Abstract

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing problems in VLSI design and identifying the optimal chain of non-overlapping fragments in bioinformatics. Using modified binary indexed tree data structure, we design an algorithm for calculating the vertex connectivity of trapezoid graph $G$ with time complexity $O (n \log n)$, where $n$ is the number of trapezoids. Furthermore, we establish sufficient and necessary condition for a trapezoid graph $G$ to be bipartite and characterize trees that can be represented as trapezoid graphs.

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Aleksandar Ilic. 2011-06-15. Efficient algorithm for the vertex connectivity of trapezoid graphs. https://arxiv.org/abs/1106.3037

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