A polynomial-time factor-2 approximation for shortest common superstring (the question behind the Tarhio-Ukkonen greedy conjecture)

Theorem 1.1: a deterministic algorithm, polynomial in the total encoded input size (including symbol labels), outputs for every finite family of explicitly represented strings a common superstring $T$ with $|T|\le2\,\mathrm{OPT}$. The proof builds a balanced hierarchical graph on all substrings from forced occurrence counts (a lower bound $W$ on the optimum), decomposes it into periodic layers and connects them at extra cost at most $W$. It does not show that Greedy or the Collapsing procedure attains factor 2 (Greedy is reported false by Shibata 2026), and gives nothing below factor 2. An August 2026 preprint of Chukhin, Kulikov, Mihajlin and Smal reported $7/3$.

Theorem 1.1: a deterministic algorithm, polynomial in the total encoded input size (including symbol labels), outputs for every finite family of explicitly represented strings a common superstring $T$ with $|T|\le2\,\mathrm{OPT}$. The proof builds a balanced hierarchical graph on all substrings from forced occurrence counts (a lower bound $W$ on the optimum), decomposes it into periodic layers and connects them at extra cost at most $W$. It does not show that Greedy or the Collapsing procedure attains factor 2 (Greedy is reported false by Shibata 2026), and gives nothing below factor 2. An August 2026 preprint of Chukhin, Kulikov, Mihajlin and Smal reported $7/3$.