TY - GEN

T1 - Navigating Weighted Regions with Scattered Skinny Tetrahedra

AU - Cheng, Siu-Wing

AU - Chiu, Man-Kwun

AU - Jin, Jiongxin

AU - Vigneron, Antoine E.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/11/27

Y1 - 2015/11/27

N2 - We propose an algorithm for finding a (1 + ε)-approximate shortest path through a weighted 3D simplicial complex T. The weights are integers from the range [1,W] and the vertices have integral coordinates. Let N be the largest vertex coordinate magnitude, and let n be the number of tetrahedra in T. Let ρ be some arbitrary constant. Let κ be the size of the largest connected component of tetrahedra whose aspect ratios exceed ρ. There exists a constant C dependent on ρ but independent of T such that if κ ≤ 1 C log log n + O(1), the running time of our algorithm is polynomial in n, 1/ε and log(NW). If κ = O(1), the running time reduces to O(nε(log(NW))).

AB - We propose an algorithm for finding a (1 + ε)-approximate shortest path through a weighted 3D simplicial complex T. The weights are integers from the range [1,W] and the vertices have integral coordinates. Let N be the largest vertex coordinate magnitude, and let n be the number of tetrahedra in T. Let ρ be some arbitrary constant. Let κ be the size of the largest connected component of tetrahedra whose aspect ratios exceed ρ. There exists a constant C dependent on ρ but independent of T such that if κ ≤ 1 C log log n + O(1), the running time of our algorithm is polynomial in n, 1/ε and log(NW). If κ = O(1), the running time reduces to O(nε(log(NW))).

UR - http://hdl.handle.net/10754/622224

UR - http://chapter/10.1007/978-3-662-48971-0_4

UR - http://www.scopus.com/inward/record.url?scp=84951939167&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-48971-0_4

DO - 10.1007/978-3-662-48971-0_4

M3 - Conference contribution

SN - 9783662489703

SP - 35

EP - 45

BT - Lecture Notes in Computer Science

PB - Springer Nature

ER -