Multi-domain network resource reservation systems are being deployed, driven by the demand and substantial benefits of providing predictable network resources. However, a major lack of existing systems is their coarse granularity, due to the participating networks' concern of revealing sensitive information, which can result in substantial inefficiencies. This paper presents Mercator, a novel multi-domain network resource discovery system to provide fine-grained, global network resource information, for collaborative sciences. The foundation of Mercator is a resource abstraction through algebraic-expression enumeration (i.e., linear inequalities/equations), as a compact representation of multiple properties of network resources (e.g., bandwidth, delay, and loss rate) in multi-domain networks. In addition, we develop an obfuscating protocol, to address the privacy concerns by ensuring that no participant can associate the algebraic expressions with the corresponding member networks. We also introduce a super-set projection technique to increase Mercator's scalability. We implement a prototype Mercator and deploy it in a small federation network. We also evaluate the performance of Mercator through extensive experiments using real topologies and traces. Results show that Mercator 1) efficiently discovers available networking resources in collaborative networks on average four orders of magnitude faster, and allows fairer allocations of network resources; 2) preserves the member networks' privacy with little overhead; and 3) scales to a collaborative network of 200 member networks.