  In this paper, we propose an algebraic approach via Lakshmibai-Seshadri (LS)
algebras to establish a link between standard monomial theories,
Newton-Okounkov bodies and valuations. This is applied to Schubert varieties,
where this approach is compatible with the one using Seshadri stratifications
by the same authors (arXiv:2112.03776), showing that LS paths encode vanishing
multiplicities with respect to the web of Schubert varieties.
