论文信息 - The approximation ratio of the greedy algorithm for the metric traveling salesman problem

The approximation ratio of the greedy algorithm for the metric traveling salesman problem

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is ? ( log n ) . Moreover, we prove that the same result also holds for graphic, euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the Clarke-Wright savings heuristic for the metric Traveling Salesman Problem is ? ( log n ) .

Stefan Hougardy | Judith Brecklinghaus | S. Hougardy | Judith Brecklinghaus

[1] Hoon Liong Ong,et al. Worst-case analysis of two travelling salesman heuristics , 1984 .

[2] Stefan Hougardy,et al. On the nearest neighbor rule for the metric traveling salesman problem , 2015, Discret. Appl. Math..

[3] Gerhard Reinelt,et al. The Traveling Salesman , 2001, Lecture Notes in Computer Science.

[4] G. Clarke,et al. Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[5] G. Reinelt. The traveling salesman: computational solutions for TSP applications , 1994 .

[6] Gerhard J. Woeginger,et al. On the nearest neighbor rule for the traveling salesman problem , 2004, Oper. Res. Lett..

[7] Richard M. Karp,et al. Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.