A simple polynomial-time rescaling algorithm for solving linear programs

The perceptron algorithm, developed mainly in the machine learning literature, is a simple greedy method for finding a feasible solution to a linear program (alternatively, for learning a threshold function). In spite of its exponential worst-case complexity, it is often quite useful, in part due to its noise-tolerance and also its overall simplicity. In this paper, we show that a randomized version of the perceptron algorithm along with periodic rescaling runs in polynomial-time. The resulting algorithm for linear programming has an elementary description and analysis.

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: John Dunagan, Santosh Vempala
• Keywords: Algorithms, Exponential Worst-case Complexity, Perceptron Algorithm, Simple Greedy Method, STOC 2004