Probe location in the presence of errors: a problem from DNA mapping
Discrete Applied Mathematics - Special volume on combinatorial molecular biology
Point placement on the line by distance data
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Fitting points on the real line and its application to RH mapping
Journal of Algorithms
The point placement problem on a line: improved bounds for pairwise distance queries
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
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Suppose that n points are located at n 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 measurements. We show that deterministic strategies cannot manage the task in two rounds with (1+o(1))n measurements in the worst case. We improve an earlier deterministic bound to roughly 4n/3 measurements.