Sublinear-competitive collective exploration of arbitrary graphs

Determine whether collective exploration of arbitrary graphs admits an algorithm with an o(k)-competitive ratio, where k is the number of agents.

Background

The paper establishes an order-optimal polylogarithmic regret bound for asynchronous collective tree exploration on trees and derives an O(log² k)-competitive algorithm for synchronous tree exploration. In contrast, the corresponding problem for arbitrary graphs is described as substantially less understood. The cited existing results do not establish whether the dependence on the number of agents k can be reduced below linear, leaving the existence of any o(k)-competitive algorithm unresolved.

References

Surprisingly, the problem of collective exploration on arbitrary graphs remains much less understood, and it is not even known whether an $o(k)$-competitive algorithm exists .

— Polylogarithmic Collective Tree Exploration  (2609.26789 - Cosson et al., 22 Sep 2026) in Section 1, Introduction, paragraph beginning “Collective tree exploration has also been studied under additional assumptions.”