Pod-Deployability in Kubernetes with Inter-Pod Affinity Constraints is PSPACE-Complete

2026-08-20

AI Summary

研究Kubernetes中考虑Pod间亲和性约束的Pod部署问题，通过分析不同约束下的复杂度，揭示了调度中的状态空间复杂性来源。

Abstract

Kubernetes is the de-facto platform for container orchestration. Its scheduler combines resource capacities with label-based affinity and anti-affinity rules, and the interaction of these features can make the eventual placement of a pod. In this paper, we study the pod-deployability problem: given an initial cluster, a pod type, and a designated node, does some legal sequence of pod deployments and deletions cover the target pair? We give three complexity results. First, when dynamic constraints contain no affinity (anti-affinity is allowed), pod-deployability is decidable in polynomial time. Second, required affinity together with required anti-affinity makes the problem PSPACE-complete. Third, required affinity alone is already enough for PSPACE-completeness on a single node with one scalar capacity. The lower bounds encode, respectively, 1-safe Petri-net coverability and bounded black pebbling. These results isolate two independent sources of state-space complexity in Kubernetes scheduling: logical exclusion and resource-bounded prerequisite management.

Problem

• pod-deployability
• kubernetes
• affinity constraints

Innovation

• PSPACE-Complete
• Inter-Pod Affinity
• Kubernetes Scheduling