A new rounding procedure for the assignment problem with applications to dense graph arrangement problems
Oct. 14, 1996 to Oct. 16, 1996
S. Arora , Dept. of Comput. Sci., Princeton Univ., NJ, USA
H. Kaplan , Dept. of Comput. Sci., Princeton Univ., NJ, USA
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 well-known 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 near-optimum fractional matchings to near-optimum 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 0-1 Quadratic Assignment problem (QAP); (ii) a (1+E)-approximation for "dense" instances of many well-known NP-hard problems, including (an optimization formulation of) GRAPH-ISOMORPHISM, MIN-CUT-LINEAR-ARRANGEMENT, MAX-ACYCLIC-SUBGRAPH, MIN-LINEAR-ARRANGEMENT, 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).
randomised algorithms; rounding procedure; assignment problem; dense graph arrangement; randomized procedure; fractional perfect matchings; linear inequality; LP rounding procedure
S. Arora, H. Kaplan, "A new rounding procedure for the assignment problem with applications to dense graph arrangement problems", FOCS, 1996, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 1996, pp. 21, doi:10.1109/SFCS.1996.548460