# The Minimum Perimeter Convex Hull of a Given Set of Disjoint Segments

• Yiyang Jia
• Bo Jiang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 691)

## Abstract

In this paper, we present an algorithm to compute the minimum perimeter convex hull of a given set of disjoint segments, so that each segment is contained in the hull completely or intersects with the boundary of the hull. The problem discussed in this paper is a novel transformation of TSP and MPSP. To solve this problem, we use a contraction strategy to contract the convex hull from a larger one which contains all endpoints of given segments to the direction of a smaller one which only contains some necessary points. We also assess the spatial relationships between outside segments and its convex hull, and add necessary segments into the convex hull successively by finding the shortest path of a sequence of segments. As a result, we present an O(n 5) algorithm for computing the minimum perimeter convex hull of a given set of disjoint segments.

## Keywords

Computational geometry Algorithm Minimum perimeter convex hull Contraction strategy

## Notes

### Acknowledgements

This work is supported by the General Project of Liaoning Province Natural Science Foundation (No. 20170540147) and Liaoning Province Science and Research (No. L2015105).

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## Authors and Affiliations

1. 1.Dalian Maritime UniversityDalianChina