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On Unknown Small Subsets and Implicit Measures: New Techniques for Parameterized Algorithms

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Abstract

Parameterized computation is a recently proposed alternative approach to dealing with NP-hard problems. Developing efficient parameterized algorithms has become a very active research area in the current research in theoretical computer science. In this paper, we investigate a number of new algorithmic techniques that were proposed and initiated by ourselves in our research in parameterized computation. The techniques have proved to be very useful and promising, and have led to improved parameterized algorithms for many well-known NP-hard problems.

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References

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

  2. Luo W, Wang J, Guo J, Chen J. Parameterized complexity of Max-lifetime Target Coverage in wireless sensor networks. Theoretical Computer Science, 2014, 518: 32–41.

    Article  MathSciNet  MATH  Google Scholar 

  3. Wang J, Luo W, Feng Q, Guo J, Chen J. Improved linear problem kernel for planar connected dominating set. Theoretical Computer Science, 2013, 511: 2–12.

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang J, Luo W, Feng Q, Guo J. Parameterized complexity of Min-power multicast problems in wireless ad hoc networks. Theoretical Computer Science, 2013, 508: 16–25.

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang J, Tan P, Yao J, Feng Q, Chen J. On the minimum link-length rectilinear spanning path problem: Complexity and algorithms. IEEE Transactions on Computers, doi.ieeecomputersociety.org/10.1109/TC.2013.163, 2013 (preprint).

  6. Ausiello G, Crescenzi P, Gambosi G, Kann V, Marchetti-Spaccamela A, Protasi M. Complexity and Approximation—Combinatorial Optimization Problems and Their Approximability Properties. Springer Verlag, 1999.

  7. Motwani R, Raghavan P. Randomized Algorithms. New York: Cambridge University Press, 1995.

    Book  MATH  Google Scholar 

  8. Michalewicz Z, Fogel D B. How to Solve It: Modern Heuristics. Berlin: Springer-Verlag, 2000.

    Book  Google Scholar 

  9. Roth-Korostensky C. Algorithms for building multiple sequence alignments and evolutionary trees [Ph.D. Thesis]. No. 13550, ETH Zöurich, 2000.

  10. Stege U. Resolving conflicts from problems in computational biology [Ph.D. Thesis]. No. 13364, ETH Zöurich, 2000.

  11. Chen J, Kanj I A, Jia W. Vertex cover: Further observations and further improvements. In Proc. Workshop on Graph-Theoretic Concepts in Computer Science-WG, Jun. 1999, pp.313–324.

  12. Chen J, Kanj I A, Xia G. Improved upper bounds for vertex cover. Theoretical Computer Science, 2010, 411(40/41/42): 3736–3756.

  13. Cheetham J, Dehne F, Rau-Chaplin A, Stege U, Taillon P J. Solving large FPT problems on coarse-granined parallel machines. Journal of Computer and System Sciences, 2003, 67(4): 691–706.

    Article  MathSciNet  MATH  Google Scholar 

  14. Lichtenstein O, Pnueli A. Checking that finite state concurrent programs satisfy their linear specification. In Proc. the 12th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, Jan. 1985, pp.97–107.

  15. Henglein F, Mairson H G. The complexity of type inference for higher-order typed lambda calculi. Journal of Functional Programming, 1994, 4(4): 435–477.

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen J, Kanj I A. Constrained minimum vertex cover in bipartite graphs: Complexity and parameterized algorithms. Journal of Computer and System Sciences, 2003, 67(4): 833–847.

    Article  MathSciNet  MATH  Google Scholar 

  17. Alon N, Yuster R, Zwick U. Color-coding. Journal of the ACM, 1995, 42(4): 844–856.

    Article  MathSciNet  MATH  Google Scholar 

  18. Dorn F, Fomin F V, Thilikos D M. Subexponential parameterized algorithms. Computer Science Review, 2008, 2(1): 29–39.

    Article  Google Scholar 

  19. Downey R, Fellows M. Parameterized Complexity. New York: Springer-Verlag, 1999.

    Book  Google Scholar 

  20. Niedermeier R. Invitation to Fixed-Parameter Algorithms. Oxford University Press, 2006.

  21. Reed B, Smith K, Vetta A. Finding odd cycle transversals. Operations Research Letters, 2004, 32(4): 299–301.

    Article  MathSciNet  MATH  Google Scholar 

  22. Kelley B P, Sharan R, Karp R M, Sittler T, Root D E, Stock-well B R, Ideker T. Conserved pathways within bacteria and yeast as revealed by global protein network alignment. Proc. Natl. Acad. Sci., 2003, 100(20): 11394–11399.

    Article  Google Scholar 

  23. Chen J, Kneis J, Lu S, Molle D, Richter S, Rossmanith P, Sze S H, Zhang F. Randomized divide-and-conquer: Improved path, matching, and packing algorithms. SIAM J. Comput., 2009, 38(6): 2526–2547.

    Article  MathSciNet  MATH  Google Scholar 

  24. Chen J, Lu S. Improved parameterized set splitting algorithms: A probabilistic approach. Algorithmica, 2009, 54(4): 472–489.

    Article  MathSciNet  MATH  Google Scholar 

  25. Kirkpatrick D G, Hell P. On the complexity of general graph factor problems. SIAM Journal on Computing, 1983, 12(3): 601–609.

    Article  MathSciNet  MATH  Google Scholar 

  26. Feng Q, Wang J, Chen J. Matching and P 2-Packing: Weighted versions. In Proc. the 17th COCOON, Aug. 2011, pp.343–353.

  27. Feng Q, Wang J, Chen J. Matching and weighted P2-Packing: Algorithms and kernels. Theoretical Computer Science, 2014, 522: 85–94.

    Article  MathSciNet  MATH  Google Scholar 

  28. Feng Q, Wang J, Li S, Chen J. Random methods for parameterized problems. In Proc. the 19th COCOON, Jun. 2013, pp.89-100.

  29. Feng Q, Wang J, Li S, Chen J. Randomized parameterized algorithms for P2-Packing and Co-Path Packing problems. Journal of Combinatorial Optimization, 2014. (to be appeared)

  30. Chen J, Lu S, Sze S H, Zhang F. Improved algorithms for path, matching, and packing problems. In Proc. the 18th Annual ACM-SIAM SODA, Jan. 2007, pp.298–307.

  31. Naor M, Schulman L, Srinivasan A. Splitters and near-optimal derandomization. In Proc. the 36th Annual Symposium on FOCS, Oct. 1995, pp.182–193.

  32. Kneis J, Möolle D, Richter S, Rossmanith P. Divide-and-color. In Proc. the 32nd Int. Workshop WG, Jun. 2006, pp.58–67.

  33. Chen J, Feng Q, Liu Y, Lu S, Wang J. Improved deterministic algorithms for weighted matching and packing problems. Theoretical Computer Science, 2011, 412(23): 2503–2512.

    Article  MathSciNet  MATH  Google Scholar 

  34. Chen J, Liu Y, Lu S, Sze S H, Zhang F. Iterative expansion and color coding: An improved algorithm for 3D-matching. ACM Transactions on Algorithms, 2012, 8(1): Article No.6.

  35. Wang J, Feng Q, Chen J. An O*(3:533k)-time parameterized algorithm for the 3-set packing problem. Theoretical Computer Science, 2011, 412(18): 1745–1753.

    Article  MathSciNet  MATH  Google Scholar 

  36. Chen J, Fomin F, Liu Y, Lu S, Villanger Y. Improved algorithms for the feedback vertex set problems. Journal of Computer and System Sciences, 2008, 74(7): 1188–1198.

    Article  MathSciNet  MATH  Google Scholar 

  37. Chen J, Liu Y, Lu S. An improved parameterized algorithm for the minimum node multiway cut problem. Algorithmica, 2009, 55(11): 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  38. Chen J, Kanj I A. On approximating minimum vertex cover for graphs with perfect matching. Theoretical Computer Science, 2005, 337(1/2/3): 305–318.

  39. Mahajan M, Raman V. Parametrizing above guaranteed values: MaxSat and MaxCut. J. Algorithms, 1999, 31(2): 335–354.

    Article  MathSciNet  MATH  Google Scholar 

  40. Mahajan M, Raman V, Sikdar S. Parameterizing MAX SNP problems above guaranteed values. In Proc. the 2nd Int. Workshop IWPEC, Sept. 2006, pp.38–49.

  41. Mahajan M, Raman V, Sikdar S. Parameterizing above or below guaranteed values. J. Comput. Syst. Sci., 2009, 75(2): 137–153.

    Article  MathSciNet  MATH  Google Scholar 

  42. Razgon I, O'Sullivan B. Almost 2-SAT is fixed-parameter tractable. Journal of Computer and System Sciences, 2009, 75(8): 435–450.

    Article  MathSciNet  MATH  Google Scholar 

  43. Wang J, Li W, Li S, Chen J. On the parameterized vertex cover problem for graphs with perfect matching. Science China Information Sciences, 2014, 57(7): 1–12.

    MathSciNet  Google Scholar 

  44. Deming R. Independence numbers of graphs—An extension of the Köonig-Egerváry theorem. Discrete Mathematics, 1979, 27(1): 23–33.

    Article  MathSciNet  MATH  Google Scholar 

  45. Chen J, Liu Y, Lu S, O'Sullivan B, Razgon I. A fixed-parameter algorithm for the directed feedback vertex set problem. Journal of the ACM, 2008, 55(5): Article No. 21.

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Correspondence to Qi-Long Feng.

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This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61173051, 61103033, and 71221061.

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Chen, J., Feng, QL. On Unknown Small Subsets and Implicit Measures: New Techniques for Parameterized Algorithms. J. Comput. Sci. Technol. 29, 870–878 (2014). https://doi.org/10.1007/s11390-014-1474-1

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  • DOI: https://doi.org/10.1007/s11390-014-1474-1

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