Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
420310 | Discrete Applied Mathematics | 2006 | 7 Pages |
Abstract
Suppose that nn points are located at nn mutually distinct but unknown positions on the line, and we can measure their pairwise distances. How many measurements are needed to determine their relative positions uniquely? The problem is motivated by DNA mapping techniques based on pairwise distance measures. It is also interesting by itself for its own and surprisingly deep. Continuing our earlier work on this problem, we give a simple randomized two-round strategy that needs, with high probability, only (1+o(1))n(1+o(1))n measurements. We show that deterministic strategies cannot manage the task in two rounds with (1+o(1))n(1+o(1))n measurements in the worst case. We improve an earlier deterministic bound to roughly 4n/34n/3 measurements.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Peter Damaschke,