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Complex event processing (CEP) evaluates queries over streams of event data to detect situations of interest. If the event data are produced by geographically distributed sources, CEP may exploit in-network processing that distributes the evaluation of a query among the nodes of a network. To this end, a query is modularized and individual query operators are assigned to nodes, especially those that act as data sources. Existing solutions for such operator placement, however, are limited in that they assume all query results to be gathered at one designated node, commonly referred to as a sink. Hence, existing techniques postulate a hierarchical structure of the network that generates and processes the event data. This largely neglects the optimisation potential that stems from truly decentralised query evaluation with potentially many sinks. To address this gap, in this paper, we propose Multi-Sink Evaluation (MuSE) graphs as a formal computational model to evaluate common CEP queries in a decentralised manner. We further prove the completeness of query evaluation under this model. Striving for distributed CEP that can scale to large volumes of high-frequency event streams, we show how to reason on the network costs induced by distributed query evaluation and prune inefficient query execution plans. As such, our work lays the foundation for distributed CEP that is both, sound and efficient. [ABSTRACT FROM AUTHOR]