Improve the Degree-Sequence Trace-Complexity Upper Bound

Improve the current $ ilde O(exp(n^{1/3}))$ trace-complexity upper bound for exact degree-sequence reconstruction from vertex-deletion traces, potentially by exploiting joint information across multiple traces rather than using information from only one vertex in each trace.

Background

The paper presents a degree-sequence reconstruction method based on rejection sampling that achieves an $exp\{\tilde O(n^{1/3})\}$ trace bound, but the method processes traces in a way that effectively extracts information from a single vertex per trace. The authors identify this as potentially wasteful.

They explicitly leave open whether joint processing of information across traces can improve the sample complexity, with recent quasipolynomial results for string trace reconstruction cited as motivation.