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《Acta Electronica Sinica》 2014-05

## Geometric Algebra-Based Algorithm for Solving Nodes Constrained Shortest Path

FENG Lin-yao;YUAN Lin-wang;LUO Wen;LI Run-chao;YU Zhao-yuan;Key Laboratory of VGE,Ministry of Education,Nanjing Normal University;Jiangsu Provincial Key Laboratory for NSLSCS,Nanjing Normal University;
Focusing on the solving of the shortest paths in the conditions of complicated constraints for network analysis and application,geometric algebra is used to develop the netw ork analysis algorithms. We built a netw ork model and bilateral search algorithms based on the multivector representation and multidimensional operators of geometric algebra. Then, w e implemented the algorithm by taking the example of finding the shortest paths that pass the specified necessary nodes and the least segments. According to the experiment analysis of the road netw ork data,this algorithm can directly estimate the constrained nodes by applying the outer algorithm and has better versatility and less path traversal times. Moreover,this algorithm has an advantage on many-to-many path solution and multi-user parallel solution.
【Fund】： 国家自然科学基金重点项目(No.41231173);; 江苏省自然科学基金(No.BK2012454);; 教育部新世纪人才培养计划(No.NECT-12-0735)
【CateGory Index】： P208;TP301.6
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