Adaptive versus nonadaptive attribute-efficient learning
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Probe location in the presence of errors: a problem from DNA mapping
Discrete Applied Mathematics - Special volume on combinatorial molecular biology
Realizing Interval Graphs with Size and Distance Constraints
SIAM Journal on Discrete Mathematics
Randomized vs. deterministic distance query strategies for point location on the line
Discrete Applied Mathematics
Randomized vs. deterministic distance query strategies for point location on the line
Discrete Applied Mathematics
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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Given partial distance information in a set of n points on the real line, we want to figure out the positions of these points, subject to translation and reflection. This type of problem is motivated by DNA mapping. We show the following results: If we can ask arbitrary distance queries for pairs of points then 2n - 3 adaptive queries will be optimal. (In contrast, all (n/2) queries must be asked in the nonadaptive case.) Surprisingly, if the learner knows in advance that the n points have distinct locations, 8/5n nonadaptive queries, or alternatively 3/2n queries in 2 rounds will be sufficient. This might be further improved, as we only have the lower bounds 4/3n and n, respectively. The subject is related to some rigidity concept for graphs. In another version of the problem, the graph of distance measures is already given, that means, we cannot choose our distance queries at our own discretion. Here, we give a simple efficient algorithm which produces a representation of all linear layouts if the given graph is chordal.