Surpass the one-half approximation barrier for online block packing

Establish whether there exists any online algorithm—either fractional or integral—for the online block packing problem with multi-dimensional resource capacities and time-discounted (quasi-patient) transaction values that achieves an approximation ratio strictly greater than 1/2 with respect to the offline optimal social welfare; equivalently, demonstrate a (1/2+ε0)-approximation for some fixed ε0>0, potentially highlighting the limits of myopic reasoning in this setting.

Background

The paper proves that a greedy fractional algorithm achieves at least half of the offline optimal social welfare, and shows matching lower bounds for broad classes of myopically-reasonable online algorithms that approach the 1/2 barrier as the number of dimensions grows. This leaves open whether any (possibly non-myopic) online strategy can strictly beat 1/2.

A result exceeding 1/2 would demonstrate that myopic block-by-block optimization is fundamentally suboptimal and that foresight or more sophisticated online decision rules are necessary to improve welfare beyond this threshold.