Approximability of compressed-length minimization in OPE/OMS

Determine whether the compressed‑length minimization variants of Optimal Pair Encoding (OPE) or Optimal Merge Sequence (OMS) admit polynomial‑time approximation algorithms with nontrivial guarantees (e.g., constant‑factor approximations), and characterize their approximability status (such as APX‑completeness).

Background

While APX-hardness extends to the compressed-length objective, the paper shows BPE does not achieve a constant-factor approximation for compressed length and leaves open whether any algorithm can do so.

Clarifying the approximability of compressed length is essential for applications where minimizing the final encoded size (rather than maximizing utility) is the primary objective.