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Randomized rounding: A technique for provably good algorithms and algorithmic proofs

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Abstract

We study the relation between a class of 0–1 integer linear programs and their rational relaxations. We give a randomized algorithm for transforming an optimal solution of a relaxed problem into a provably good solution for the 0–1 problem. Our technique can be a of extended to provide bounds on the disparity between the rational and 0–1 optima for a given problem instance.

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References

  1. R. Aharoni, P. Erdős andN. Linial, Dual Integer Linear Programs and the Relationship between their Optima,Proceedings of the Seventeenth ACM Symposium on Theory of Computing, ACM, New York, May1985, 476–483.

    Chapter  Google Scholar 

  2. D. Angluin andL. G. Valiant, Fast probabilistic algorithms for Hamiltonian circuits and matchings,Journal of Computer and System Sciences,19, 155–193.

  3. H. Chernoff, A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations,Annals of Math. Stat.,23 (1952), 493–509.

    MathSciNet  Google Scholar 

  4. S. Even, A. Itai andA. Shamir, On the complexity of timetable and multi-commodity flow problems,SIAM Journal on Computing,5 (1976), 691–703.

    Article  MATH  MathSciNet  Google Scholar 

  5. Z. Füredi, Maximum degree and fractional matchings in uniform hypergraphs,Combinatorica 1 (1981), 155–162.

    MATH  MathSciNet  Google Scholar 

  6. W. Hoeffding, On the distribution of the number of successes independent trials,Annals of Math. Stat.,27 (1956), 713–721.

    MathSciNet  Google Scholar 

  7. T. C. Hu andM. T. Shing, A Decomposition Algorithm for Circuit Routing,Mathematical Programming Study,24 (1985), 87–103.

    MATH  MathSciNet  Google Scholar 

  8. N. Karmarkar, A new polynomial-time algorithm for linear programming,Combinatorica 4 (1984), 373–396.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. M. Karp, Reducibility among combinatorial problems,Complexity of Computer Computations, (ed. R. N. Miller, J. W. Thatcher),Plenum Press, New York, (1972), 85–104.

    Google Scholar 

  10. R. M. Karp, F. T. Leighton, R. L. Rivest, C. D. Thompson, U. Vazirani andV. Vazirani Global Wire Routing in Two-Dimensional Arrays,Proc. 24th Annual Symp. on Foundations of Computer Science, (1983), 453–459.

  11. L. Lovász, On the ratio of optimal and fractional covers,Discrete Mathematics,13 (1975), 383–390.

    Article  MATH  MathSciNet  Google Scholar 

  12. V. M. Malhotra, M. P. Kumar andS. N. Maheshwari, AnO(|V|3) algorithm for finding maximum flows in networks,Information Processing Letters,7 (1978), 277–278.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Raghavan andC. D. Thompson, Randomized Routing in Gate-Arrays,CSD/84/202, Computer Science Division, UC Berkeley, (1984).

  14. P. Raghavan andC. D. Thompson, Provably Good Routing in Graphs: Regular Arrays,Proceedings of the Seventeenth ACM Symposium on Theory of Computing, ACM, New York, (1985), 79–87.

  15. P. Raghavan, Randomized Rouding and Discrete Ham-Sandwiches: Provably Good Algorithms for Routing and Packing Problems,PhD Thesis, Computer Science Division, UC Berkeley, (1986).

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This work was supported by Semiconductor Research Corporation grant SRC 82-11-008 and an IBM Doctoral Fellowship.

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Raghavan, P., Tompson, C.D. Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica 7, 365–374 (1987). https://doi.org/10.1007/BF02579324

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  • DOI: https://doi.org/10.1007/BF02579324

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