The complexity of binary matrix completion under diameter constraints

We thoroughly study a novel but basic combinatorial matrix completion problem: Given binary incomplete matrix, fill in the missing entries so that every pair of rows resulting has Hamming distance within specified range. obtain an almost complete picture complexity landscape regarding constraints and maximum number any row. develop polynomial-time algorithms for diameter three based on Deza's theorem [Discret. Math. 1973] from extremal set theory. also prove NP-hardness at least four. For per row, we show solvability when there is only one can be two. In many our algorithms, heavily rely to identify sunflower structures. This paves way towards which are finding graph factors solving 2-SAT instances.