Linear And Hereditary Discrepancy

Let A be an m × n matrix and q := ⌊log2(m)⌋+1. In this article we improve the well-known bound lindisc(A) ≤ 2 herdisc(A) and show thatformula hereAs with the previous proofs relating to this problem, ours is constructive. We will give an on-line algorithm and analyse it using game theory.