Proceedings ArticleDOI
Finding Longest (s, t)-paths of O-shaped Supergrid Graphs in Linear Time
Ruo-Wei Hung,Fatemeh Keshavarz-Kohjerdi,Yuh-Min Tseng,Guo-Hao Qiu +3 more
- pp 8923400
TLDR
A linear-time algorithm is proposed to find the longest (s, t)-path of O-shaped supergrid graphs, which can be used to compute the smallest stitching path of computerized embroidery machine and 3D printer when a hollow object is printed.Abstract:
The longest path and Hamiltonian problems were known to be NP-complete. In spite of many applications of these problems, their complexities are still unknown for many classes of graphs, including supergrid graphs with holes and solid supergrid graphs. In this paper, we will study the complexity of the longest (s, t)-path problem on O-shaped supergrid graphs. The longest (s, t)-path is a simple path from s to t with the largest number of visited vertices. An O-shaped supergrid graph is a rectangular supergrid graph with one rectangular hollow. We will propose a linear-time algorithm to find the longest (s, t)-path of O-shaped supergrid graphs. The longest (s, t)-paths of O-shaped supergrid graphs can be used to compute the smallest stitching path of computerized embroidery machine and 3D printer when a hollow object is printed.read more
Citations
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Journal ArticleDOI
The Longest (s, t)-Path Problem on O-Shaped Supergrid Graphs
TL;DR: In this paper , a linear-time algorithm was proposed to solve the longest (s,t)-path problem on O-shaped supergrid graphs with holes. But the complexity of solving the shortest path problem on these graphs is unknown.
Journal ArticleDOI
The Hamiltonicity and Hamiltonian-connectivity of Solid Supergrid Graphs
Proceedings Article
The Hamiltonian Connectivity of Rectangular Supergrid Graphs
TL;DR: A constructive proof is provided to show that rectangular supergrid graphs are Hamiltonian connected except one trivial forbidden condition and a linear-time algorithm is presented to construct a longest path between any two given vertices in a rectangular super grid graph.
References
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Book
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Journal ArticleDOI
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