Partial info yields 20% better facility assignments, new paper shows

A new paper from Vasilis Gkatzelis, Hasti Karimi, Emma Rewinski, Maziar Shamsipour, and Alexandros A. Voudouris tackles the classic facility assignment problem under a pragmatic constraint: only partial information about the metric is available. The problem involves placing agents (e.g., customers) to facilities (e.g., service centers) along a line to minimize social cost (total distance traveled). Prior work focused solely on ordinal preferences (agents rank facilities). This team expands the information types to include approval preferences (which facilities are acceptable) and inter-facility distances, and asks how much these extra signals can reduce the distortion—the worst-case ratio of the algorithm's cost to the optimal cost.

Their results are tight for deterministic algorithms. With only ordinal info, no algorithm can beat distortion 3. Adding approval info doesn't help alone. But combining approval preferences with inter-facility distances yields distortion 1+√2 (≈2.414), a 19.5% improvement, and this bound holds even for general metrics, not just lines. When all three information types are available, the distortion drops to exactly 2. These findings provide a clear theoretical framework for designing robust assignment algorithms under realistic data constraints.