Extend the algorithms to weakly lexicographic valuations with ties

Investigate whether the algorithmic results for lexicographic valuations extend to weakly lexicographic valuations that permit indifference, or ties, between items.

Background

The paper's algorithms rely substantially on strict lexicographic preferences and the resulting domination and mutual-exclusion properties. In particular, strict value gaps ensure strict comparisons between bundles and enable the pruning arguments used by the exact algorithms.

Weakly lexicographic valuations allow ties between items, potentially disrupting these structural arguments. The unresolved problem is therefore to determine whether comparable approximation or exact-algorithmic guarantees remain valid in this broader valuation domain.