2015/02/02 by Wenhong Tian, Tian, Wenhong, Chaojie Huang +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Algorithm #Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #Genome Rearrangement Algorithms #Optimization and Packing Problems #Vehicle Routing Optimization Methods #cs.DS
paper · pdf · doi:10.48550/arxiv.1502.00447
10 pages
openalex publication_date 2015/02/02 · openalex created_date 2016/06/24 · arxiv created 2016/12/12 · arxiv updated 2016/12/13 · openalex updated_date 2026/07/28
The traveling salesman problem (TSP) is one of the most challenging NP-hard problems. It has widely applications in various disciplines such as physics, biology, computer science and so forth. The best known approximation algorithm for Symmetric TSP (STSP) whose cost matrix satisfies the triangle inequality (called \triangleSTSP) is Christofides algorithm which was proposed in 1976 and is a (3)/(2)-approximation. Since then no proved improvement is made and improving upon this bound is a fundamental open question in combinatorial optimization. In this paper, for the first time, we propose Truncated Generalized Beta distribution (TGB) for the probability distribution of optimal tour lengths in a TSP. We then introduce an iterative TGB approach to obtain quality-proved near optimal approximation, i.e., (1+(1)/(2)((α+1)/(α+2))K-1)-approximation where K is the number of iterations in TGB and α(>>1) is the shape parameters of TGB. The result can approach the true optimum as K increases.