Sub-2 Polynomial-Time Approximation for Maximum Multipacking

Determine whether Maximum Multipacking on general graphs admits a polynomial-time approximation algorithm with approximation factor strictly below 2, or prove that the factor 2 is computationally tight.

Background

The paper establishes a polynomial-time factor-2 approximation algorithm for Maximum Multipacking and notes that Multipacking is NP-complete on general graphs. It also shows that the factor 2 in the relation between broadcast domination and multipacking is best possible as a parameter bound, with equality for cycles and ratios tending to 2 for an infinite family of hypercubes.

The unresolved algorithmic question is whether the approximation guarantee can be improved below 2 in polynomial time, or whether no such improvement is possible unless the relevant complexity-theoretic assumptions fail.

References

Since Multipacking is NP-complete on general graphs , it is natural to ask whether an approximation algorithm with factor strictly below $2$ is possible in polynomial time, or whether it is tight.

— Broadcast Domination Number is at Most Twice the Multipacking Number  (2608.20036 - Islam, 20 Aug 2026) in Section Conclusion