分布式约束满足问题的复杂性
The Complexity of the Distributed Constraint Satisfaction Problem
摘要：
本文从理论上研究了同步匿名网络上分布式约束满足问题的复杂性。在这种设置中，变量和约束由代理控制，代理通过固定的通信信道发送消息来相互通信。我们的研究结果认可了经典CSP中的一个众所周知的事实，即固定模板计算问题的复杂性取决于模板在某些操作下的不变性。具体来说，我们表明，DCSP（$Γ$）是多项式时间易处理的当且仅当$Γ$是不变的对称多态性的所有arities。否则，没有在有限时间内求解DCSP（$Γ$）的算法。我们还表明，同样的条件适用于搜索变种的DCSP。附带地，我们的研究结果揭示了一个功能的进程的邻域在分布式网络，其迭代度，这在分析中起着重要作用。我们探讨这个概念建立一个紧密的连接与基本的线性规划放松的CSP。
英文摘要：
We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with each other by sending messages through fixed communication channels. Our results endorse the well-known fact from classical CSPs that the complexity of fixed-template computational problems depends on the template's invariance under certain operations. Specifically, we show that DCSP($Γ$) is polynomial-time tractable if and only if $Γ$ is invariant under symmetric polymorphisms of all arities. Otherwise, there are no algorithms that solve DCSP($Γ$) in finite time. We also show that the same condition holds for the search variant of DCSP. Collaterally, our results unveil a feature of the processes' neighbourhood in a distributed network, its iterated degree, which plays a major role in the analysis. We explore this notion establishing a tight connection with the basic linear programming relaxation of a CSP.
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