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Decremental Approximate-APSP in Directed Graphs

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Encyclopedia of Algorithms
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  1. Baswana S, Hariharan R, Sen S (2007) Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths. J Algorithms 62(2):74–92

    Article  MathSciNet  MATH  Google Scholar 

  2. Bernstein A (2009) Fully dynamic approximate all-pairs shortest paths with constant query and close to linear update time. In: Proceedings of the 50th FOCS, Atlanta, pp 50–60

    Google Scholar 

  3. Bernstein A (2013) Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]. In: STOC, Palo Alto, pp 725–734

    MATH  Google Scholar 

  4. Bernstein A, Roditty L (2011) Improved dynamic algorithms for maintaining approximate shortest paths under deletions. In: Proceedings of the 22nd SODA, San Francisco, pp 1355–1365

    Google Scholar 

  5. Demetrescu C, Italiano GF (2004) A new approach to dynamic all pairs shortest paths. J ACM 51(6):968–992. doi:http://doi.acm.org/10.1145/1039488.1039492

  6. Fredman ML, Tarjan RE (1987) Fibonacci heaps and their uses in improved network optimization algorithms. J ACM 34(3):596–615

    Article  MathSciNet  Google Scholar 

  7. Henzinger M, Krinninger S, Nanongkai D (2013) Dynamic approximate all-pairs shortest paths: breaking the o(mn) barrier and derandomization. In: FOCS 2013, Berkeley, pp 538–547

    Google Scholar 

  8. Henzinger M, Krinninger S, Nanongkai D (2014) Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs. In: STOC, New York, pp 674–683

    MATH  Google Scholar 

  9. Henzinger M, Krinninger S, Nanongkai D (2014) A subquadratic-time algorithm for decremental single-source shortest paths. In: SODA 2014, Portland

    Google Scholar 

  10. King V (1999) Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In: FOCS, New York, pp 81–91

    Google Scholar 

  11. Pettie S (2004) A new approach to all-pairs shortest paths on real-weighted graphs. Theor Comput Sci 312(1):47–74. doi:10.1016/S0304-3975(03)00402-X, http://dx.doi.org/10.1016/S0304-3975(03)00402-X

  12. Roditty L, Zwick U (2012) Dynamic approximate all-pairs shortest paths in undirected graphs. SIAM J Comput 41(3):670–683

    Article  MathSciNet  MATH  Google Scholar 

  13. Takaoka T (1992) A new upper bound on the complexity of the all pairs shortest path problem. Inf Process Lett 43(4):195–199. doi:10.1016/0020-0190(92)90200-F, http://dx.doi.org/10.1016/0020-0190(92)90200-F

  14. Williams R (2014) Faster all-pairs shortest paths via circuit complexity. In: STOC, New York, pp 664–673

    MATH  Google Scholar 

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Bernstein, A. (2016). Decremental Approximate-APSP in Directed Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_564

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