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On the greedy walk problem

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Abstract

This note introduces a greedy walk on Poisson and Binomial processes, which is a close relative to the well-known greedy server model. Some open problems are presented.

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References

  1. Beardwood, J., Halton, J.H., Hammersley, J.M.: The shortest path through many points. Proc. Camb. Philos. Soc. 55, 299–327 (1959)

    Article  Google Scholar 

  2. Bentley, J.L., Saxe, J.B.: An analysis of two heuristics for the Euclidean traveling salesman problem. In: Proc. 18th Allerton Conference on Communication, Control and Computing, vol. 6, pp. 41–49. University of Illinois, Urbana-Champaign (1980)

    Google Scholar 

  3. Bertsimas, D.J., Garrett van Ryzin, G.: A stochastic and dynamic vehicle routing problem in the Euclidean plane. Oper. Res. 39, 601–615 (1991)

    Article  Google Scholar 

  4. Coffman, E.G. Jr., Gilbert, E.N.: Polling and greedy servers on a line. Queueing Syst. 2, 115–145 (1987)

    Article  Google Scholar 

  5. Foss, S., Last, G.: Stability of polling systems with exhaustive service policies and state dependent routing. Ann. Appl. Probab. 6, 116–137 (1996)

    Article  Google Scholar 

  6. Foss, S., Last, G.: On the stability of greedy polling systems with general service policies. Probab. Eng. Inf. Sci. 12, 49–68 (1998)

    Article  Google Scholar 

  7. Rojas-Nandayapa, L., Foss, S., Kroese, D.: Stability and performance of greedy server systems: A review and open problems. Queueing Syst., this volume (2011)

  8. Rosenkrantz, D., Stearns, R., Lewis, P.: An analysis of several heuristics for the traveling salesman problem. SIAM J. Comput. 6(5), 563–581 (1977)

    Article  Google Scholar 

  9. Schassberger, R.: Stability of polling networks with state-depending server routing. Probab. Eng. Inf. Sci. 9, 539–550 (1995)

    Article  Google Scholar 

  10. Steele, J.M.: Cost of sequential connection for points in space. Oper. Res. Lett. 8(3), 137–142 (1989)

    Article  Google Scholar 

  11. Steele, J.M.: Probability Theory and Combinatorial Optimization. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 69. SIAM, Philadelphia (1997)

    Google Scholar 

  12. Yukich, J.: Probability Theory of Classical Euclidean Optimization Problems. Lecture Notes in Mathematics, vol. 1675. Springer, Berlin (1998)

    Google Scholar 

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Correspondence to Charles Bordenave.

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Bordenave, C., Foss, S. & Last, G. On the greedy walk problem. Queueing Syst 68, 333–338 (2011). https://doi.org/10.1007/s11134-011-9246-x

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  • DOI: https://doi.org/10.1007/s11134-011-9246-x

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