A 3/2-Approximation Algorithm for the Multiple TSP with a Fixed Number of Depots
We study a natural extension of the classical traveling salesman problem (TSP) in the situation where multiple salesmen are dispatched from a number of different depots. As with the TSP, this problem is motivated by a large range of applications in vehicle routing. Although it is known to have a 2-approximation algorithm, whether the problem has a 3/2-approximation algorithm, as is the case with the well-known Christofides heuristic for the TSP, remains an open question. We answer this question positively by providing a 3/2-approximation algorithm for the problem with a fixed number of depots. The algorithm uses an edge exchange strategy, and its analysis hinges on a newly discovered exchange property of matroids. In addition, the algorithm is applied to multidepot extensions of other TSP variants, and we show for the first time, to our knowledge, that for these multidepot extensions the same best constant approximation ratios can be achieved as for their respective single-depot cases.
approximation algorithm, multiple depots, traveling salesman, matroid
Operations and Supply Chain Management
INFORMS Journal on Computing
INFORMS (Institute for Operations Research and Management Sciences)
XU, Zhou and RODRIGUES, Brian Charles.
A 3/2-Approximation Algorithm for the Multiple TSP with a Fixed Number of Depots. (2015). INFORMS Journal on Computing. 27, (4), 636-645. Research Collection Lee Kong Chian School Of Business.
Available at: http://ink.library.smu.edu.sg/lkcsb_research/4921