Deep investigation of greedy algorithms are started at the end if 1990s with joint works of V. Temlyakov and S. Konyagin. They, together with N. Kalton, P. Wojtaszczyk and S. Dilworth introduced bases with different kind of efficiency of greedy algorithm and proved several important results. In that theory there were 2 weak aspects that doesn't allow to do further investigation
1. Does X-greedy algorithm converge for functions from $L^p$, $1 < p \neq 2 < \infty$ with respect to the Haar system.
2. Construct effective gredy type algorithms in $L^1$.
The first question was partially answered by E. Livshitz.
During this seminar we will talk about second question and will provide about methods that allow to give answer to several ideas. Those methods allow to obtain global conclusions based on the local behavior of Haar coefficients.