Years and Authors of Summarized Original Work
1987; Raghavan, Thompson
Problem Definition
Randomized rounding is a technique for designing approximation algorithms for NP-hard optimization problems. Many combinatorial optimization problems can be represented as 0-1 integer linear programs; that is, integer linear programs in which variables take values in \( { \{0,1\} } \). While 0-1 integer linear programming is NP-hard, the rational relaxations (also referred to as fractional relaxations) of these linear programs are solvable in polynomial time [12, 13]. Randomized rounding is a technique to construct a provably good solution to a 0-1 integer linear program from an optimum solution to its rational relaxation by means of a randomized algorithm.
Let Î be a 0-1 integer linear program with variables \( { x_i \in \{0,1\} } \), \( { 1 \le i \le n } \). Let Î R be the rational relaxation of Î obtained by replacing the \( { x_i \in \{0,1\} } \) constraints by \( { x_i \in [0,1], 1 \le i \le...
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Rajaraman, R. (2016). Randomized Rounding. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_327
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