Direct weighted extension of the semi-streaming auction algorithm

Extend Algorithm 1, the auction-based semi-streaming algorithm for unweighted matroid intersection, directly to the weighted matroid intersection setting in order to obtain improved weighted matroid intersection algorithms.

Background

The paper develops auction-based algorithms for unweighted and weighted matroid intersection. Its principal semi-streaming algorithm, Algorithm 1, achieves a deterministic near-optimal approximation for unweighted matroid intersection using a constant number of passes and space linear in the matroid intersection rank. The paper extends the unweighted result to weighted matroid intersection only indirectly, through a reduction due to Dudeja and Grilnberger, which incurs additional dependence on the weight aspect ratio and approximation parameter.

The unresolved issue is whether the semi-streaming auction mechanism itself can be adapted directly to weighted matroid intersection, potentially avoiding the overhead of the reduction and yielding improved weighted algorithms.