Applications of combinatorial programming to data analysis: The traveling salesman and related problems

The “Traveling Salesman” and similar combinatorial programming tasks encountered in operations research are discussed as possible data analysis models in psychology, for example, in developmental scaling, Guttman scaling, profile smoothing, and data array clustering. In addition, a short overview of the various computational approaches from this area of combinatorial optimization is included.

[1]  Helmut Steckhan.  A Theorem on Symmetric Traveling Salesman Problems , 1970, Oper. Res..

[2]  A. Bagchi,et al.  Neighborhood search algorithms for finding optimal traveling salesman tours must be inefficient , 1973, STOC.

[3]  T. A. J. Nicholson,et al.  A Sequential Method for Discrete Optimization Problems and its Application to the Assignment, Travelling Salesman, and Three Machine Scheduling Problems , 1967 .

[4]  T. C. Raymond.  Heuristic algorithm for the traveling-salesman problem , 1969 .

[5]  Selmer M. Johnson,et al.  On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem , 1959 .

[6]  L. Hubert.  SERIATION USING ASYMMETRIC PROXIMITY MEASURES , 1976 .

[7]  H. Wainer,et al.  TWO ADDITIONS TO HIERARCHICAL CLUSTER ANALYSIS , 1972 .

[8]  Mandell Bellmore,et al.  Pathology of Traveling-Salesman Subtour-Elimination Algorithms , 1971, Oper. Res..

[9]  S. M. Roberts,et al.  An Engineering Approach to the Traveling Salesman Problem , 1966 .

[10]  Lawrence Hubert,et al.  Problems of seriation using a subject by item response matrix. , 1974 .

[11]  G. Croes.  A Method for Solving Traveling-Salesman Problems , 1958 .

[12]  G. Mensch.  Single-Stage Linear Programming Zero-One Solutions to Some Travelling Salesman Type Problems* , 1971 .

[13]  Clyde H. Coombs,et al.  On the detection of structure in attitudes and developmental processes. , 1973 .

[14]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

[15]  Efraim Turban,et al.  Letter to the Editor - Some Comments on the Traveling Salesman Problem , 1969, Oper. Res..

[16]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[17]  Lawrence Hubert,et al.  SOME APPLICATIONS OF GRAPH THEORY AND RELATED NON‐METRIC TECHNIQUES TO PROBLEMS OF APPROXIMATE SERIATION: THE CASE OF SYMMETRIC PROXIMITY MEASURES , 1974 .

[18]  James R. Slagle,et al.  A Clustering and Data-Reorganizing Algorithm , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  Bert F. Green,et al.  A method of scalogram analysis using summary statistics , 1956 .

[20]  Richard Bellman,et al.  Dynamic Programming Treatment of the Travelling Salesman Problem , 1962, JACM.

[21]  Patrick D. Krolak,et al.  A man-machine approach toward solving the traveling salesman problem , 1970, CACM.

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

[23]  Nicos Christofides,et al.  Algorithms for Large-scale Travelling Salesman Problems , 1972 .

[24]  John J. Wiorkowski,et al.  A rapid heuristic algorithm for the approximate solution of the traveling salesman problem , 1975 .

[25]  G. L. Thompson,et al.  A Heuristic Approach to Solving Travelling Salesman Problems , 1964 .

[26]  P. Arabie,et al.  An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling , 1975 .

[27]  D. Kendall.  Abundance matrices and seriation in archaeology , 1971 .

[28]  P. C. Sagi.  A statistical test for the significance of a coefficient of reproducibility , 1959 .

[29]  Robert S. Garfinkel,et al.  Technical Note - On Partitioning the Feasible Set in a Branch-and-Bound Algorithm for the Asymmetric Traveling-Salesman Problem , 1973, Oper. Res..

[30]  J. William Gavett,et al.  Three Heuristic Rules for Sequencing Jobs to a Single Production Facility , 1965 .

[31]  E. Kay,et al.  Graph Theory. An Algorithmic Approach , 1975 .

[32]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[33]  Alan E. Gelfand,et al.  Seriation Methods for Archaeological Materials , 1971, American Antiquity.

[34]  Olav Solem,et al.  Contribution to the solution of sequencing problems in process industry , 1974 .

[35]  L. L. Barachet.  Letter to the Editor---Graphic Solution of the Traveling-Salesman Problem , 1957 .

[36]  S. N. Narahari Pandit,et al.  Letter to the Editor-Some Observations on the Longest Path Problem , 1964 .

[37]  Alex Karel Obruca.  Spanning Tree Manipulation and the Travelling Salesman Problem , 1968, Comput. J..

[38]  Richard C. T. Lee,et al.  Experiments with some cluster analysis algorithms , 1974, Pattern Recognit..

[39]  M. M. Flood.  The Traveling-Salesman Problem , 1956 .

[40]  D. Kendall,et al.  Mathematics in the Archaeological and Historical Sciences , 1971, The Mathematical Gazette.

[41]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[42]  Paul J. Schweitzer,et al.  Problem Decomposition and Data Reorganization by a Clustering Technique , 1972, Oper. Res..

[43]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[44]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[45]  E. Bowden.  Ordinal scaling of multicategory persisting and disappearing traits , 1973 .

[46]  Jan Karel Lenstra,et al.  Some Simple Applications of the Travelling Salesman Problem , 1975 .

[47]  L. Hubert,et al.  Quadratic assignment as a general data analysis strategy. , 1976 .

[48]  A. H. Land,et al.  A Contribution to the “Travelling‐Salesman” Problem , 1955 .

[49]  Jan Karel Lenstra,et al.  Technical Note - Clustering a Data Array and the Traveling-Salesman Problem , 1974, Oper. Res..

[50]  A. Gelfand.  Rapid seriation methods for multivariate observations through similarities , 1974 .

[51]  M. V. Bhat,et al.  An Efficient Clustering Algorithm , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[52]  J. N. Allen.  Low overhead sequencing algorithm , 1969 .

[53]  Nicos Christofides,et al.  Hamiltonian Circuits and the Travelling Salesman Problem , 1975 .

[54]  Katta G. Murty,et al.  On the Tours of a Traveling Salesman , 1969 .

[55]  T. A. J. Nicholson.  A Boundary Method for Planar Travelling Salesman Problems , 1968 .

[56]  George L. Nemhauser,et al.  The Traveling Salesman Problem: A Survey , 1968, Oper. Res..

[57]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[58]  W. W. Hardgrave,et al.  On the Relation Between the Traveling-Salesman and the Longest-Path Problems , 1962 .

[59]  Nicos Christofides,et al.  Technical Note - Bounds for the Travelling-Salesman Problem , 1972, Oper. Res..

[60]  Jakob Krarup,et al.  Improvements of the Held—Karp algorithm for the symmetric traveling-salesman problem , 1974, Math. Program..

[61]  Nicos Christofides,et al.  The Shortest Hamiltonian Chain of a Graph , 1970 .