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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1990: STACS 90 pp 298–311Cite as

The analysis of local search problems and their heuristics

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References

  1. E. R. Barnes, A. Vanelli and J. Q. Walker, A New Heuristic for Partitioning the Nodes of a Graph, SIAM J. Disc. Math. 1(1988), pp. 299–305.

    Article  Google Scholar 

  2. J. L. Bentley, Experiments on Traveling Salesman Heuristics, Proc. First ACM-SIAM Symposium on Discrete Algorithms, 1990.

    Google Scholar 

  3. J. L. Bentley, D. S. Johnson, L. A. McGeosh and E. E. Rothberg, Near Optimal Solutions to Very Large Traveling Salesman Problems, in preparation, 1990.

    Google Scholar 

  4. J. Bruck and J. W. Goodman, A Generalized Convergence Theorem for Neural Networks, IEEE Trans. Inf. Theory 34(1988), pp. 1089–1092.

    Article  Google Scholar 

  5. A. Condon, Computational Models of Games, MIT Press, 1989.

    Google Scholar 

  6. A. E. Dunlop and B. W. Kernighan, A Procedure for Placement of Standard-Cell VLSI Circuits IEEE Trans. CAD 4(1985), pp. 92–98.

    Google Scholar 

  7. C. M. Fiduccia and R. M. Mattheyses, A Linear-Time Heuristic for Improving Network Partitions, Proc. 19th Annual Design Automation Conference, 1982, pp. 175–181.

    Google Scholar 

  8. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, 1979.

    Google Scholar 

  9. J. R. Gilbert and E. Zmijewski, A Parallel Graph Partitioning Algorithm for a Message-Passing Multiprocessor, Intl. J. Paral. Prog. 16(1987), pp. 427–449.

    Article  Google Scholar 

  10. G. Godbeer, On the Computational Complexity of the Stable Configuration Problem for Connectionist Models, Master's Thesis, Dept. of Comp. Sci., U. of Toronto, September, 1987.

    Google Scholar 

  11. E. Goles-Chacc, F. Fogelman-Soulie and D. Pellegrin, Decreasing Energy Functions as a Tool for Studying Threshold Networks, Discrete Appl. Math. 12(1985), pp. 261–277.

    Article  Google Scholar 

  12. E. Goles and J. Olivos, The Convergence of Symmetric Threshold Automata, Information and Control 51(1981), pp. 98–104.

    Article  Google Scholar 

  13. M. Grotschel, L. Lovasz and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer Verlag, 1988.

    Google Scholar 

  14. A. Haken and M. Luby, Steepest Descent Can Take Exponential Time for Symmetric Connection Networks, Complex Systems 2(1988), pp. 191–196.

    Google Scholar 

  15. J. J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Nat. Acad. Sci. 79(1982), pp. 2554–2558.

    PubMed  Google Scholar 

  16. J. J. Hopfield and D. W. Tank, Neural Computation of Decisions in Optimization Problems, Biol. Cyber. 52(1985), pp. 141–152.

    Google Scholar 

  17. D. Howard, Dynamic Programming and Markov Processes, MIT Press, 1960.

    Google Scholar 

  18. R. J. Jeroslow, The Simplex Algorithm with the Pivot Rule of Maximizing Criterion Improvement, Disc. Math. 4(1973), pp. 367–378.

    Article  Google Scholar 

  19. D. S. Johnson, C. R. Aragon, L. A McGeoch, and C. Schevon, Optimization By Simulated Annealing: An Experimental Evaluation, Part I (Graph Partitioning), Operations Research, to appear.

    Google Scholar 

  20. D. S. Johnson, C. R. Aragon, L. A McGeoch, and C. Schevon, Optimization By Simulated Annealing: An Experimental Evaluation, Part II (Graph Coloring and Number Partitioning), manuscript, 1989.

    Google Scholar 

  21. D. S. Johnson, C. R. Aragon, L. A McGeoch, and C. Schevon, Optimization By Simulated Annealing: An Experimental Evaluation, Part III (The Traveling Salesman Problem), in preparation, 1990.

    Google Scholar 

  22. D. S. Johnson, C. H. Papadimitriou, M. Yannakakis, How Easy Is Local Search?, J. Comp. Syst. Sci. 37(1988), pp. 79–100.

    Article  Google Scholar 

  23. N. Karmarkar, A New Polynomial Time Algorithm for Linear Programming, Combinatorica 4(1984), pp. 373–395.

    Google Scholar 

  24. R. M. Karp and A. Wigderson, A Fast Parallel Algorithm for the Maximal Independent Set Problem, J. Assoc. Comput. Mach. 32(1985), pp. 762–773.

    Google Scholar 

  25. W. Kern, A Probabilistic Analysis of the Switching Algorithm for the Euclidean TSP, Mathematical Programming 44(1989), pp. 213–219.

    Google Scholar 

  26. B. Kemighan and S. Lin, An Efficient Heuristic Procedure for Partitioning Graphs, Bell Syst. Tech. J. 49(1970), pp. 291–307.

    Google Scholar 

  27. L. G. Khachian, A Polynomial Algorithm for Linear Programming, Soviet Math. Doklady 20(1979), pp. 191–194.

    Google Scholar 

  28. S. Kirkpatrick, C. Gelat, and M. Vecchi, Optimization by Simulated Annealing, Science 220(1983), pp. 671–680.

    Google Scholar 

  29. V. Klee and G. J. Minty, How Good is the Simplex Algorithm?, in Inequalities III, O. Shisha, ed., Academic Press, 1971.

    Google Scholar 

  30. V. Klee and D. W. Walkup, The d-step Conjecture for Polyhedra of Dimension d<6, Acta Math. 117(1967), pp. 53–78.

    Google Scholar 

  31. J. H. M. Korst and E. H. L. Aarts, Combinatorial Optimization on a Boltzman Machine, J. Parallel and Distr. Comp. 6(1989), pp. 331–357.

    Google Scholar 

  32. M. W. Krentel, On Finding Locally Optimal Solutions, Proc. 4th Annual Structure in Complexity Conference, 1989, pp. 132–137; also to appear in SIAM J. Comp.

    Google Scholar 

  33. M. W. Krentel, Structure in Locally Optimal Solutions, Proc. 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 216–221.

    Google Scholar 

  34. S. Lin, Computer Solutions of the Traveling Salesman Problem, Bell Syst. Tech. J. 44(1965), pp. 2245–2269.

    Google Scholar 

  35. S. Lin and B. Kemighan, An Effective Heuristic for the Traveling Salesman problem, Oper. Res. 21(1973), pp. 498–516.

    Google Scholar 

  36. J. Lipscomb, On the Computational Complexity of Finding a Connectionist Model's Stable State of Vectors, Master's Thesis, Dept. of Comp. Sci., U. of Toronto, October, 1987.

    Google Scholar 

  37. D. C. Llewellyn, C. Tovey and M. Trick, Local Optimization on Graphs, Discrete Appl. Math. (1989).

    Google Scholar 

  38. M. Luby, A Simple Parallel Algorithm for the Maximal Independent Set Problem, SIAM J. Comp. 15(1986), pp. 1036–1053.

    Google Scholar 

  39. G. Lueker, manuscript, Princeton University (1976).

    Google Scholar 

  40. J. J. More and S. A. Vavasis, On the Solution of Concave Knapsack Problems, Preprint, Argonne National Laboratory, (1988).

    Google Scholar 

  41. K. G. Murty and S. N. Kabadi, Some NP-complete Problems in Quadratic and Nonlinear Programming, Mathematical Programming 39(1987), pp. 117–129.

    Google Scholar 

  42. C. H. Papadimitriou, The Complexity of the Lin-Kemighan Heuristic for the Traveling Salesman Problem, manuscript, (1989).

    Google Scholar 

  43. C. H. Papadimitriou and K. Steiglitz, Some Examples of Difficult Traveling Salesman Problems, Oper. Res. 26(1978), pp. 434–443.

    Google Scholar 

  44. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, 1982.

    Google Scholar 

  45. I. Parberry, A Primer on the Complexity Theory of Neural Networks, to appear in A Sourcebook on Formal Techniques in Artificial Intelligence, R. B. Banerji, ed., Elsevier, 1989.

    Google Scholar 

  46. P. M. Pardalos and G. Schnitger, Checking Local Optimality in Constrained Quadratic Programming is NP-hard, Oper. Res. Let. 7(1988), pp. 33–35.

    Google Scholar 

  47. V. Rodl and C. Tovey, Multiple Optima in Local Search, J. of Algorithms 8(1987), pp. 250–259.

    Google Scholar 

  48. G. H. Sasaki and B. Hajek, The Time Complexity of Maximum Matching by Simulated Annealing, J. Assoc. Comput. Mach. 35(1988), pp. 387–403.

    Google Scholar 

  49. A. A. Schaffer and M. Yannakakis, Simple Local Search Problems That Are Hard to Solve, manuscript, (1989).

    Google Scholar 

  50. M. J. Todd, The Monotonic Bounded Hirsch Conjecture is False for Dimension At Least 4, Math. Oper. Res. 5(1980), pp. 599–601.

    Google Scholar 

  51. C. A. Tovey, Hill Climbing with Multiple Local Optima, SIAM J. Alg. Disc. Meth. 6(1985), pp. 384–393.

    Google Scholar 

  52. C. A. Tovey, Low Order Polynomial Bounds on the Expected Performance of Local Improvemnet Algorithms, Mathematical Programming 35(1986), pp. 193–224.

    Google Scholar 

  53. J. D. Ullman and A. Van Gelder, Efficient Tests for Top-Down Termination of Logical Rules, J. Assoc. Comp. Mach. 35(1988), pp. 345–373.

    Google Scholar 

  54. P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Practice, Kluwer Academic Publishers, 1987.

    Google Scholar 

  55. J. van Leeuwen and A. A. Schoone, Untangling a Traveling Salesman Tour in the Plane, Technical Report RUU-CS-80-11, University of Utrecht (1980).

    Google Scholar 

  56. A. Vergis, K. Steiglitz and B. Dickinson, The Complexity of Analog Computation, Math. and Comp. in Simulation 28(1986), pp. 91–113.

    Google Scholar 

  57. V. G. Vizing, Complexity of the Traveling Salesman Problem in the Class of Monotonic Improvement Algorithms, Eng. Cyb. 4(1978), pp. 623–626.

    Google Scholar 

  58. P. Weiner, S. L. Savage and A. Bagchi, Neighborhood Search Algorithms for Guaranteeing Optimal Traveling Salesman Tours Must be Inefficient, J. Comp. Sys. Sci. 12(1976), pp. 25–35.

    Google Scholar 

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Authors and Affiliations

  1. AT&T Bell Laboratories, 07974, Murray Hill, NJ, U.S.A.

    Mihalis Yannakakis

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  1. Mihalis Yannakakis
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Christian Choffrut Thomas Lengauer

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© 1990 Springer-Verlag Berlin Heidelberg

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Yannakakis, M. (1990). The analysis of local search problems and their heuristics. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_52

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  • DOI: https://doi.org/10.1007/3-540-52282-4_52

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  • Print ISBN: 978-3-540-52282-9

  • Online ISBN: 978-3-540-46945-2

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