带有 Pod 间亲和性约束的 Kubernetes 中 Pod 可部署性问题是 PSPACE 完全问题
Pod-Deployability in Kubernetes with Inter-Pod Affinity Constraints is PSPACE-Complete
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中文总结 AI 辅助
本文研究 Kubernetes 中 Pod 可部署性问题，证明仅必需亲和性或其与反亲和性结合时该问题为 PSPACE 完全问题，分离出调度中状态空间复杂度的两个独立来源。
中文摘要 AI 辅助
Kubernetes 是容器编排的事实标准平台，其调度器结合资源容量与基于标签的亲和性、反亲和性规则，这些特征的相互作用会影响 Pod 的最终部署位置。本文研究 Pod 可部署性问题：给定初始集群、一种 Pod 类型和指定节点，是否存在合法的 Pod 部署与删除序列能覆盖目标配对？我们给出三个复杂度结果：第一，当动态约束不含亲和性（允许反亲和性）时，Pod 可部署性问题可在多项式时间内判定；第二，必需亲和性与必需反亲和性结合使该问题成为 PSPACE 完全问题；第三，仅必需亲和性在具有一个标量容量的单个节点上已足以让问题成为 PSPACE 完全问题。这些下界分别编码了 1-安全 Petri 网的覆盖性与有界黑 pebbling。这些结果分离出 Kubernetes 调度中状态空间复杂度的两个独立来源：逻辑排斥与资源受限的先决条件管理。
英文摘要
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.
