ISAAC 2010: Algorithms and Computation pp 109-120

# Approximate Shortest Homotopic Paths in Weighted Regions

• Siu-Wing Cheng
• Jiongxin Jin
• Antoine Vigneron
• Yajun Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6507)

## Abstract

Let P be a path between two points s and t in a polygonal subdivision $$\mathcal T$$ with obstacles and weighted regions. Given a relative error tolerance ε ∈ (0,1), we present the first algorithm to compute a path between s and t that can be deformed to P without passing over any obstacle and the path cost is within a factor 1 + ε of the optimum. The running time is $$O(\frac{h^3}{\varepsilon^2}kn\,\mathrm{polylog}(k,n,\frac{1}{\varepsilon}))$$, where k is the number of segments in P and h and n are the numbers of obstacles and vertices in $$\mathcal T$$, respectively. The constant in the running time of our algorithm depends on some geometric parameters and the ratio of the maximum region weight to the minimum region weight.

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## Authors and Affiliations

• Siu-Wing Cheng
• 1
• Jiongxin Jin
• 1
• Antoine Vigneron
• 2
• Yajun Wang
• 3
1. 1.Department of Computer Science and EngineeringHKUSTHong Kong
2. 2.INRAUR 341 Mathématiques et Informatique AppliquéesJouy-en-JosasFrance
3. 3.Microsoft Research AsiaBeijingChina