Abstract
We present the first approximation algorithm for a two depot, heterogeneous traveling salesman problem with an approximation ratio of 3 when the costs are symmetric and satisfy the triangle inequality.
Similar content being viewed by others
References
Chandler, P., Pachter, M.: Research issues in autonomous control of tactical UAVs. In: Proceedings of the American Control Conference, pp. 394–398 (1998)
Chandler, P., Pachter, M., Swaroop, D., Fowler, J.M., Howlett, J.K., Rasmussen, S., Schumacher, C., Nygard, K.: Complexity in UAV cooperative control. In: Proceedings of the American Control Conference, pp. 1831–1836 (2002)
Lagoudakis, M., Markakis, V., Kempe, D., Keskinocak, P., Koenig, S., Kleywegt, A., Tovey, C., Meyerson, A., Jain, S.: Auction-based multi-robot routing. In Proceedings of the International Conference on Robotics: Science and Systems, pp. 343–350 (2005)
Tisdale, J., Ryan, A., Zennaro, M., Xiao, X., Caveney, D., Rathinam, S., Hedrick, J.K., Sengupta, R.: The software architecture of the Berkeley UAV platform. In: IEEE Conference on Control Applications, Munich, Germany (2006)
Gutin, G., Punnen, A.P. (eds): The Travelling Salesman Problem and its Variations. Kluwer Academic Publishers, Dordrecht (2002)
Gutin G.: Traveling Salesman Problem. In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization, pp. 3935–3944. Springer, USA (2009)
Vazirani V.V.: Approximation Algorithms. Springer, Berlin (2001)
Du, D., Pardalos, P. M. (eds). Handbook of Combinatorial Optimization, vol. 1–3 (1999)
Marinakis Y.: Heuristic and Metaheuristic Algorithms for the Traveling Salesman Problem. In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization, pp. 1498–1506. Springer, USA (2009)
Lawler E.L.: Combinatorial Optimization: Networks and Matroids. Dover Publications, USA (2001)
Reinelt G.: The Traveling Salesman-Computational Solutions for TSP Allocations, Lecture Notes in Computer Science 840. Springer, Berlin (1994)
Christofides, N.: Worst-case analysis of a new heuristic for the Traveling Salesman Problem, Technical Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh (1976)
Malik W., Rathinam S., Darbha S.: An approximation algorithm for a symmetric generalized multiple depot, multiple travelling salesman problem. Oper. Res. Lett. 35(6), 747–753 (2007)
Rathinam S., Sengupta R., Darbha S.: A resource allocation algorithm for multi-vehicle systems with non-holonomic constraints. IEEE Trans. Autom. Sci. Eng. 4(1), 98–104 (2007)
Rathinam, S., Sengupta, R.: Lower and upper bounds for a multiple depot UAV Routing Problem. In: IEEE Control and Decision Conference, San Diego, California (2006)
Rathinam S., Sengupta R.: 3/2-approximation algorithm for two variants for a 2-Depot, Hamiltonian path problem. Oper. Res. Lett. 38(1), 63–68 (2010)
Xu, Z., Rodrigues, B.: A 3/2-approximation algorithm for multiple depot multiple traveling salesman problem, algorithm theory—SWAT 2010, Lecture Notes in Computer Science, Springer Berlin/Heidelberg vol. 6139, pp. 127–138 (2010)
Yadlapalli, S., Rathinam, S., Darbha, S.: An approximation algorithm for a heterogenous, multiple vehicle, multiple travelling salesman problem. American Control Conference (2009)
Menger K.: Zur allgemeinen Kurventheorie. Fund. Math. 10, 96–115 (1927)
Grotschel M., Lovasz L., Schrijver A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2), 169–197 (1981)
Shmoys D.B., Williamson D.P.: Analyzing the Held-Karp TSP bound: a monotonicity property with application. Inf. Process. Lett. 35(6), 281–285 (1990)
Goemans M.X., Bertsimas D.: Survivable networks, linear programming relaxations and the parsimonius property. Math. Program. 60, 143–166 (1993)
Ford L.R. Jr., Fulkerson D.R.: Flows in Networks. Princeton University Press, Princeton (1962)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yadlapalli, S., Rathinam, S. & Darbha, S. 3-Approximation algorithm for a two depot, heterogeneous traveling salesman problem. Optim Lett 6, 141–152 (2012). https://doi.org/10.1007/s11590-010-0256-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-010-0256-0