We consider variable selection techniques for high-dimensional survival data. We develop five algorithms for variable selection suitable for right censored data. The approaches can be used for parameter estimation and prediction for survival time with both low and high–dimensional data. The first two algorithms are based on a synthesis of the Buckley–James methods and the Dantzig Selector. The remaining algorithms are based on the weighted Dantzig selector where weights are obtained using the synthesis based algorithms. The algorithms are simple and scalable. The algorithms can deal with collinearity among the covariates and also among the groups of the covariates. We conduct several simulation studies and one empirical analysis with a microarray dataset. The proposed algorithms work very well for selecting sparse model or smaller variable subsets under many practical conditions.