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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.
J. L. Bentley, Experiments on Traveling Salesman Heuristics, Proc. First ACM-SIAM Symposium on Discrete Algorithms, 1990.
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.
J. Bruck and J. W. Goodman, A Generalized Convergence Theorem for Neural Networks, IEEE Trans. Inf. Theory 34(1988), pp. 1089–1092.
A. Condon, Computational Models of Games, MIT Press, 1989.
A. E. Dunlop and B. W. Kernighan, A Procedure for Placement of Standard-Cell VLSI Circuits IEEE Trans. CAD 4(1985), pp. 92–98.
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.
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, 1979.
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.
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.
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.
E. Goles and J. Olivos, The Convergence of Symmetric Threshold Automata, Information and Control 51(1981), pp. 98–104.
M. Grotschel, L. Lovasz and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer Verlag, 1988.
A. Haken and M. Luby, Steepest Descent Can Take Exponential Time for Symmetric Connection Networks, Complex Systems 2(1988), pp. 191–196.
J. J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Nat. Acad. Sci. 79(1982), pp. 2554–2558.
J. J. Hopfield and D. W. Tank, Neural Computation of Decisions in Optimization Problems, Biol. Cyber. 52(1985), pp. 141–152.
D. Howard, Dynamic Programming and Markov Processes, MIT Press, 1960.
R. J. Jeroslow, The Simplex Algorithm with the Pivot Rule of Maximizing Criterion Improvement, Disc. Math. 4(1973), pp. 367–378.
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.
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.
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.
D. S. Johnson, C. H. Papadimitriou, M. Yannakakis, How Easy Is Local Search?, J. Comp. Syst. Sci. 37(1988), pp. 79–100.
N. Karmarkar, A New Polynomial Time Algorithm for Linear Programming, Combinatorica 4(1984), pp. 373–395.
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.
W. Kern, A Probabilistic Analysis of the Switching Algorithm for the Euclidean TSP, Mathematical Programming 44(1989), pp. 213–219.
B. Kemighan and S. Lin, An Efficient Heuristic Procedure for Partitioning Graphs, Bell Syst. Tech. J. 49(1970), pp. 291–307.
L. G. Khachian, A Polynomial Algorithm for Linear Programming, Soviet Math. Doklady 20(1979), pp. 191–194.
S. Kirkpatrick, C. Gelat, and M. Vecchi, Optimization by Simulated Annealing, Science 220(1983), pp. 671–680.
V. Klee and G. J. Minty, How Good is the Simplex Algorithm?, in Inequalities III, O. Shisha, ed., Academic Press, 1971.
V. Klee and D. W. Walkup, The d-step Conjecture for Polyhedra of Dimension d<6, Acta Math. 117(1967), pp. 53–78.
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.
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.
M. W. Krentel, Structure in Locally Optimal Solutions, Proc. 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 216–221.
S. Lin, Computer Solutions of the Traveling Salesman Problem, Bell Syst. Tech. J. 44(1965), pp. 2245–2269.
S. Lin and B. Kemighan, An Effective Heuristic for the Traveling Salesman problem, Oper. Res. 21(1973), pp. 498–516.
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.
D. C. Llewellyn, C. Tovey and M. Trick, Local Optimization on Graphs, Discrete Appl. Math. (1989).
M. Luby, A Simple Parallel Algorithm for the Maximal Independent Set Problem, SIAM J. Comp. 15(1986), pp. 1036–1053.
G. Lueker, manuscript, Princeton University (1976).
J. J. More and S. A. Vavasis, On the Solution of Concave Knapsack Problems, Preprint, Argonne National Laboratory, (1988).
K. G. Murty and S. N. Kabadi, Some NP-complete Problems in Quadratic and Nonlinear Programming, Mathematical Programming 39(1987), pp. 117–129.
C. H. Papadimitriou, The Complexity of the Lin-Kemighan Heuristic for the Traveling Salesman Problem, manuscript, (1989).
C. H. Papadimitriou and K. Steiglitz, Some Examples of Difficult Traveling Salesman Problems, Oper. Res. 26(1978), pp. 434–443.
C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, 1982.
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.
P. M. Pardalos and G. Schnitger, Checking Local Optimality in Constrained Quadratic Programming is NP-hard, Oper. Res. Let. 7(1988), pp. 33–35.
V. Rodl and C. Tovey, Multiple Optima in Local Search, J. of Algorithms 8(1987), pp. 250–259.
G. H. Sasaki and B. Hajek, The Time Complexity of Maximum Matching by Simulated Annealing, J. Assoc. Comput. Mach. 35(1988), pp. 387–403.
A. A. Schaffer and M. Yannakakis, Simple Local Search Problems That Are Hard to Solve, manuscript, (1989).
M. J. Todd, The Monotonic Bounded Hirsch Conjecture is False for Dimension At Least 4, Math. Oper. Res. 5(1980), pp. 599–601.
C. A. Tovey, Hill Climbing with Multiple Local Optima, SIAM J. Alg. Disc. Meth. 6(1985), pp. 384–393.
C. A. Tovey, Low Order Polynomial Bounds on the Expected Performance of Local Improvemnet Algorithms, Mathematical Programming 35(1986), pp. 193–224.
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.
P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Practice, Kluwer Academic Publishers, 1987.
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).
A. Vergis, K. Steiglitz and B. Dickinson, The Complexity of Analog Computation, Math. and Comp. in Simulation 28(1986), pp. 91–113.
V. G. Vizing, Complexity of the Traveling Salesman Problem in the Class of Monotonic Improvement Algorithms, Eng. Cyb. 4(1978), pp. 623–626.
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.
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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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