Abstract
Dynamic data structures are presented for directed graphs that maintain (a) Transitive Closure and (b) Decomposition into Strongly Connected Components in a “semi-online” situation which improve the static algorithms for minimum sum-of-diameters clustering are improved by a O(log n) factor.
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References
B. Aspvall, M.F. Plass and R.E. Tarjan. A Linear-time Algorithm for Testing the Truth of Certain Quantified Boolean Expressions, IPL, 8, 1979, pp 121–123.
S. Cicerone, D. Frigioni, U Nanni and F Pugliese. A uniform approach to semi-dynamic problems on digraphs, TCS, 203, 1998, pp 69–90.
S. R. Doddi, M. V. Marathe, S. S. Ravi, D. S. Taylor and P. Widmayer. Approximation algorithms for clustering to minimize the sum of diameters. In Proc. of 7th SWAT, 2000, LNCS vol 1851, pp 237–250.
C. Demetrescu and G.F. Italiano. Fully Dynamic Transitive Closure: Breaking Through the O(n 2) barrier, 41st IEEE FOCS pp. 381–389.
P. Hansen and B. Jaumard. Minimum Sum of Diameters Clustering, Journal of Classification, 4:215–226, 1987.
P. Hansen and B. Jaumard. Cluster analysis and mathematical programming, Mathematical Programming, 79, 1997, pp 191–215.
S. Khanna, R. Motwani and R.H. Wilson. On certificates and lookahead on dynamic graph problems, Proc 7th ACM-SIAM Symp. Discr. Algthms, 1996, pp222–231.
V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. Proc. 40th IEEE FOCS, 1999.
V. King and G. Sagert. A Fully Dynamic Algorithm for Maintaining the Transitive Closure, ACM STOC 1999, pp 492–498.
C. Monma and S. Suri. Partitioning Points and Graphs to Minimize the Maximum or the Sum of Diameters, Proc. 6th Intl. Conf. on Theory and Applications of Graphs, Kalamazoo, Michigan, May 1989, pp 899–912.
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© 2002 Springer-Verlag Berlin Heidelberg
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Ramnath, S. (2002). Forewarned Is Fore-Armed: Dynamic Digraph Connectivity with Lookahead Speeds Up a Static Clustering Algorithm. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_23
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DOI: https://doi.org/10.1007/3-540-45471-3_23
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