Tractable instances of Min Saturated Pebbling

Investigate whether tractable instances of Min Saturated Pebbling exist despite the problem’s NP-hardness in the general case.

Background

The paper defines Min Saturated Pebbling as the problem of finding a minimum-size saturated pebbling of a variation graph, where selecting an edge requires assigning it all colors corresponding to paths that traverse it. Unlike unrestricted Min Pebbling, Min Saturated Pebbling is shown to be NP-hard, even when every predefined path has at most three edges, and is reduced to Minimum-Weight Set Cover and an integer linear programming formulation.

The authors explicitly identify the existence of tractable instances as an unresolved direction, leaving open the characterization of graph or path-structure restrictions under which Min Saturated Pebbling can be solved efficiently.