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Towards an abstract parallel branch and bound machine

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Solving Combinatorial Optimization Problems in Parallel

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References

  1. O.J. Boxma, G.A.P. Kindervater (1991). A queueing network model for analyzing a class of branch-and-bound algorithms on a master-slave architecture. Oper. Res. 39, 1005–1017.

    Google Scholar 

  2. J. Clausen, J.L. Träff (1991). Implementation of parallel branch and bound algorithms — experiences with the graph partitioning problem. Ann. Oper. Res. 33, 341–349.

    Article  Google Scholar 

  3. R. Corrêa, A. Ferreira (1995). Parallel best-first branch-and-bound in discrete optimization: a framework. A. Ferreira, P.M. Pardalos (eds.). Solving Combinatorial Optimization Problems in Parallel, Lecture Notes in Computer Science, Springer, Berlin, this volume.

    Google Scholar 

  4. V.-D. Cung, S. Dowaji, B. Le Cun, C. Roucairol (1995). The outcome of a know-how: a branch-and-bound library. A. Ferreira, P.M. Pardalos (eds.). Solving Combinatorial Optimization Problems in Parallel, Lecture Notes in Computer Science, Springer, Berlin, this volume.

    Google Scholar 

  5. A. de Bruin, H.W.J.M. Trienekens (1992). Towards a Taxonomy of Parallel Branch and Bound Algorithms, Report EUR-CS-92-01, Department of Computer Science, Erasmus University, Rotterdam.

    Google Scholar 

  6. W.L. Eastman (1958). Linear Programming with Pattern Constraints, Report BL 20, The Computation Laboratory, Harvard University, Cambridge.

    Google Scholar 

  7. R. Finkel, U. Manber (1987). DIB — a distributed implementation of backtracking. ACM Trans. Prog. Lang. and Syst. 9, 235–256.

    Article  Google Scholar 

  8. P.C. Gilmore (1962). Optimal and suboptimal algorithms for the quadratic assignment problem. J. Soc. Indust. Apl. Math. 10, 305–313.

    Article  Google Scholar 

  9. T. Ibaraki (1976). Theoretical comparisons of search strategies in branch-and-bound algorithms. Int. J. Comput. Inform. Sci. 5, 315–344.

    Article  Google Scholar 

  10. T. Ibaraki (1977a). On the computational efficiency of branch-and-bound algorithms. J. Oper. Res. Soc. Japan 20, 16–35.

    Google Scholar 

  11. T. Ibaraki (1977b). The power of dominance relations in branch-and-bound algorithms. J. Assoc. Comput. Mach. 24, 264–279.

    Google Scholar 

  12. T. Ibaraki (1978). Branch-and-bound procedure and state-space representation of combinatorial optimization problems. Inf. Control 36, 1–27.

    Article  Google Scholar 

  13. J.M. Jansen, F.W. Sijstermans (1989). Parallel branch-and-bound algorithms. Future Generations Comput. Syst. 4, 271–279.

    Article  Google Scholar 

  14. G.A.P. Kindervater (1991). Exercises in Parallel Combinatorial Computing, CWI Tract 78, Centre for Mathematics and Computer Science, Amsterdam.

    Google Scholar 

  15. N. Kuck, M. Middendorf, H. Schmeck (1993). Generic branch-and-bound on a network of transputer. R. Grebe et. al. (eds.). Transputer Applications and Systems '93, IOS Press, 521–535.

    Google Scholar 

  16. V. Kumar, L.N. Kanal (1983). A general branch and bound formulation for understanding and synthesizing And/Or tree search procedures. Art. Intelligence 21, 179–198.

    Google Scholar 

  17. A.H. Land, A.G. Doig (1960). An automatic method for solving discrete programming problems. Econometrica 28, 497–520.

    Google Scholar 

  18. E.L. Lawler, D.E. Wood (1966). Branch-and-bound methods: a survey. Oper. Res. 14, 699–719.

    Google Scholar 

  19. G.-J. Li, B.W. Wah (1986). Coping with anomalies in parallel branch-and-bound algorithms. IEEE Trans. Comput. C-35, 568–573.

    MathSciNet  Google Scholar 

  20. J.D.C. Little, K.G. Murty, D.W. Sweeney, C. Karel (1963). An algorithm for the traveling salesman problem. Oper. Res. 11, 972–989.

    Google Scholar 

  21. G.P. McKeown, V.J. Rayward-Smith, H.J. Turpin (1991). Branch-and-bound as a higher-order function. Ann. Oper. Res. 33, 379–402.

    Article  Google Scholar 

  22. D.L. Miller, J.F. Pekny (1989). Results from a parallel branch and bound algorithm for the asymmetric traveling salesman problem. Oper. Res. Lett. 8, 129–135.

    Article  Google Scholar 

  23. L.G. Mitten (1970). Branch-and-bound methods: general formulation and properties. Oper. Res. 18, 24–34.

    Google Scholar 

  24. D.S. Nau, V. Kumar, L.N. Kanal (1984). General branch and bound and its relation to A* and AO*. Art. Intelligence 23, 29–58.

    Article  Google Scholar 

  25. V.J. Rayward-Smith, S.A. Rush, G.P. McKeown (1993). Efficiency considerations in the implementation of parallel branch-and-bound. Ann. Oper. Res. 43, 123–145.

    Article  MathSciNet  Google Scholar 

  26. M.J. Rossman, R.J. Twery, F.D. Stone (1958). A Solution to the Traveling Salesman Problem by Combinatorial Programming, Peat, Marwick, Mitchell and Co., Chicago (mimeographed).

    Google Scholar 

  27. D.R. Smith (1984). Random trees and the analysis of branch and bound procedures. J. Assoc. Comput. Mach. 31, 163–188.

    MathSciNet  Google Scholar 

  28. H.C. Tijms (1986). Stochastic Modeling and Analysis: a Computational Approach, Wiley, Chichester.

    Google Scholar 

  29. H.W.J.M. Trienekens (1990). Parallel Branch and Bound Algorithms, Ph.D. thesis, Erasmus University, Rotterdam.

    Google Scholar 

  30. O. Vornberger (1987). Load balancing in a network of transputers. Proc. 2nd Int. Workshop on Distributed Algorithms, LNCS 312, Springer, Berlin, 116–126.

    Google Scholar 

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Afonso Ferreira Panos Pardalos

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de Bruin, A., Kindervater, G.A.P., Trienekens, H.W.J.M. (1996). Towards an abstract parallel branch and bound machine. In: Ferreira, A., Pardalos, P. (eds) Solving Combinatorial Optimization Problems in Parallel. Lecture Notes in Computer Science, vol 1054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027121

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  • DOI: https://doi.org/10.1007/BFb0027121

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