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We propose a theoretical analysis of a novel source routing scheme called XSR. XSR uses linear encoding operation to both (1) build the path labels of unicast and multicast data transfers; (2) perform fast computational efficient routing decisions compared to standard table lookup procedure without any packet modification all along the path. XSR specifically focuses on decreasing the computational complexity of forwarding operations. This allows packet switches (e.g, link-layer switch or router) to perform only simple linear operations over a binary vector label that embeds the path. We provide analytical proofs demonstrating that XSRs efficiently compute a valid unicast or multicast path label over any finite fields F 2 w . Furthermore, we show that this path label can be used for both the forward and return unicast paths, unlike other source routing algorithms that require recomputing a label for the return path. Compared to recent approaches based on modular arithmetic, XSR computes the smallest label possible and presents strong scalable properties, allowing it to be deployed over any kind of core vendor or datacenter networks. [ABSTRACT FROM AUTHOR]