Exact reachability with unbounded pod multiplicities

Determine whether unbounded multiplicities of zero-request pod types in exact Kubernetes cluster-configuration reachability can be handled by a different finite abstraction, and determine the resulting complexity of the exact reachability problem.

Background

The paper studies pod-deployability as a coverability property: whether some reachable configuration contains at least one instance of a target pod type on a designated node. Exact configuration reachability is a stricter problem because it specifies the complete target configuration, including the absence and multiplicity of every other pod type.

For capacity-bounded instances, the configuration graph is finite and configurations have polynomial-size representations, yielding a PSPACE upper bound by exploration. However, without binding capacities, zero-request pod types can be deployed in arbitrarily large multiplicities. The support abstraction used for the paper’s capacity-free affinity and anti-affinity analysis collapses all positive multiplicities and is sound for coverability but not for exact reachability. The paper leaves open whether another finite abstraction can preserve the multiplicity information required by exact reachability and what complexity classification would follow.