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41st Annual Symposium on Foundations of Computer Science
Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
C. Demetrescu, G.F. Italiano, "Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 381, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892126, author = {C. Demetrescu and G.F. Italiano}, title = {Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {381}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892126}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier SN  02725428 SP EP A1  C. Demetrescu, A1  G.F. Italiano, PY  2000 KW  directed graphs; polynomials; matrix multiplication; computational complexity; randomised algorithms; deterministic algorithms; fully dynamic transitive closure; polynomials; matrix multiplication; deterministic algorithm; directed graphs; unit worstcase cost; queries; amortized time; directed acyclic graphs; singleoperation complexity; subquadratic algorithm; randomized algorithm VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive closure, in particular we devise a deterministic algorithm for general directed graphs that achieves O(n/sup 2/) amortized time for updates, while preserving unit worstcase cost for queries. In case of deletions only, our algorithm performs updates faster in O(n) amortized time. Our matrixbased approach yields an algorithm for directed acyclic graphs which breaks through the O(n/sup 2/) barrier on the singleoperation complexity of fully dynamic transitive closure. We can answer queries in O(n/sup /spl epsiv//) time and perform updates in O(n/sup /spl omega/(1,/spl epsiv/,1)/spl epsiv//+n/sup 1+/spl epsiv//) time, for any /spl epsiv//spl isin/[0,1], where /spl omega/(1,/spl epsiv/,1) is the exponent of the multiplication of an n/spl times/n/sup /spl epsiv// matrix by an n/sup /spl epsiv///spl times/n matrix. The current best bounds on /spl omega/(1,/spl epsiv/,1) imply an O(n/sup 0.575/) query time and an O(n/sup 1.575/) update time. Our subquadratic algorithm is randomized, and has oneside error.
Index Terms:
directed graphs; polynomials; matrix multiplication; computational complexity; randomised algorithms; deterministic algorithms; fully dynamic transitive closure; polynomials; matrix multiplication; deterministic algorithm; directed graphs; unit worstcase cost; queries; amortized time; directed acyclic graphs; singleoperation complexity; subquadratic algorithm; randomized algorithm
Citation:
C. Demetrescu, G.F. Italiano, "Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier," focs, pp.381, 41st Annual Symposium on Foundations of Computer Science, 2000
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