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 the available bandwidth 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. Finally, we implement Mercator and demonstrate both its efficiency and efficacy through extensive experiments using real topologies and traces.