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37th Annual Symposium on Foundations of Computer Science (FOCS '96)
A new rounding procedure for the assignment problem with applications to dense graph arrangement problems
Burlington, VT
October 14October 16
ISBN: 0818675942
ASCII Text  x  
S. Arora, A. Frieze, H. Kaplan, "A new rounding procedure for the assignment problem with applications to dense graph arrangement problems," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 21, 37th Annual Symposium on Foundations of Computer Science (FOCS '96), 1996.  
BibTex  x  
@article{ 10.1109/SFCS.1996.548460, author = {S. Arora and A. Frieze and H. Kaplan}, title = {A new rounding procedure for the assignment problem with applications to dense graph arrangement problems}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1996}, isbn = {0818675942}, pages = {21}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1996.548460}, 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  A new rounding procedure for the assignment problem with applications to dense graph arrangement problems SN  0818675942 SP EP A1  S. Arora, A1  A. Frieze, A1  H. Kaplan, PY  1996 KW  randomised algorithms; rounding procedure; assignment problem; dense graph arrangement; randomized procedure; fractional perfect matchings; linear inequality; LP rounding procedure VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional matching satisfies any linear inequality, then with high probability, the new matching satisfies that linear inequality in an approximate sense. This extends the wellknown LP rounding procedure of Raghavan and Thompson (1987), which is usually used to round fractional solutions of linear programs. It also solves an open problem of Luby and Nisan (1993) ("Design an NC procedure for converting nearoptimum fractional matchings to nearoptimum matchings.") We use the rounding procedure to design n/sup 0(logn//spl epsiv/(2)/) time algorithms for the following: (i) an additive approximation to the 01 Quadratic Assignment problem (QAP); (ii) a (1+E)approximation for "dense" instances of many wellknown NPhard problems, including (an optimization formulation of) GRAPHISOMORPHISM, MINCUTLINEARARRANGEMENT, MAXACYCLICSUBGRAPH, MINLINEARARRANGEMENT, and BETWEENNESS. (A "dense" graph is one in which the number of edges is /spl Omega/(n/sup 2/); denseness for the other problems is defined in an analogous way).
Index Terms:
randomised algorithms; rounding procedure; assignment problem; dense graph arrangement; randomized procedure; fractional perfect matchings; linear inequality; LP rounding procedure
Citation:
S. Arora, A. Frieze, H. Kaplan, "A new rounding procedure for the assignment problem with applications to dense graph arrangement problems," focs, pp.21, 37th Annual Symposium on Foundations of Computer Science (FOCS '96), 1996
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