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Distance estimation is important to many Internet applications. It can aid a World Wide Web client when selecting among several potential candidate servers or among candidate peer-to-peer servers. It can also aid in building efficient overlay or peer-to-peer networks that react dynamically to changes in the underlying Internet. One of the approaches to distance (i.e., time delay) estimation in the Internet is based on placing tracer stations in key locations and conducting measurements between them. The tracers construct an approximated map of the Internet after processing the information obtained from these measurements. This work presents a novel algorithm, based on algebraic tools, that computes additional distances, which are not explicitly measured. As such, the algorithm extracts more information from the same amount of measurement data. Our algorithm has several practical impacts. First, it can reduce the number of tracers and measurements without sacrificing information. Second, our algorithm is able to compute distance estimates between locations where tracers cannot be placed. To evaluate the algorithm's performance, we tested it both on randomly generated topologies and on real Internet measurements. Our results show that the algorithm computes up to 50%-200% additional distances beyond the basic tracer-to-tracer measurements.