Special cases of the traveling salesman problem

The paper surveys special cases of the traveling salesman problem that are in the literature. The tables include polynomial time recognition algorithms and relationships among special cases. As a result of research, the most general special cases are identified. The paper also contains a table of subclasses of the most general special cases. Applications and open questions are indicated.

[1]  R. H. Warren Optimal arcs for the traveling salesman problem , 1992 .

[2]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[3]  Kenneth Kalmanson Edgeconvex Circuits and the Traveling Salesman Problem , 1975, Canadian Journal of Mathematics.

[4]  V. S. Aizenshtat,et al.  Certain classes of traveling-salesman problems , 1978 .

[5]  Hansjoachim Walther,et al.  The assignment and the travelling salesman problems , 1984 .

[6]  R. Burkard SPECIAL CASES OF TRAVELLING SALESMAN PROBLEMS AND HEURISTICS , 1990 .

[7]  Rainer E. Burkard,et al.  Travelling Salesman and Assignment Problems: A Survey , 1979 .

[8]  M. Cutler Efficient special case algorithms for the n-line planar traveling salesman problem , 1980, Networks.

[9]  Ting-Yi Sung,et al.  A polynomial-time solution to Papadimitriou and Steiglitz's 'traps' , 1988 .

[10]  Günter Rote,et al.  Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane , 1987, ICALP.

[11]  R. H. Warren Classes of matrices for the traveling salesman problem , 1990 .

[12]  Günter Rote,et al.  The Convex-Hull-and-Line Traveling Salesman Problem: A Solvable Case , 1994, Inf. Process. Lett..

[13]  Ramaswamy Chandrasekaran Recognition of Gilmore-Gomory traveling salesman problem , 1986, Discret. Appl. Math..

[14]  E. Lawler,et al.  Well-solved special cases , 1985 .

[15]  R. Burkard,et al.  Universal Conditions for Algebraic Traveling Salesman Problems to be Efficiently Solvable , 1991 .

[16]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[17]  V. K. Leont'ev Stability of the travelling salesman problem , 1975 .

[18]  M. Held,et al.  A dynamic programming approach to sequencing problems , 1962, ACM National Meeting.

[19]  A. Volgenant,et al.  Nonoptimal Edges for the Symmetric Traveling Salesman Problem , 1984, Oper. Res..

[20]  Miłosz Michalski On a class of polynomially solvable travelling salesman problems , 1987 .

[21]  Günter Rote The n-line traveling salesman problem , 1992, Networks.

[22]  A. Volgenant,et al.  Identification of non-optimal arcs for the travelling salesman problem , 1982, Oper. Res. Lett..