TY - GEN
T1 - Fitting Distances by Tree Metrics Minimizing the Total Error within a Constant Factor
AU - Cohen-Addad, Vincent
AU - Das, Debarati
AU - Kipouridis, Evangelos
AU - Parotsidis, Nikos
AU - Thorup, Mikkel
N1 - Funding Information:
The full version of the paper can be accessed at https://arxiv.org/ abs/2110.02807 Research of Debarati Das, Evangelos Kipouridis and Mikkel Thorup is supported by VILLUM Investigator Grant 16582, Basic
Funding Information:
Evangelos Kipouridis has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 801199. 1https://iep.utm.edu/classifi/, Internet Encyclopedia of Philosophy
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - We consider the numerical taxonomy problem of fitting a positive distance function D}:\binom{S2rightarrow R}> 0 by a tree metric. We want a tree T with positive edge weights and including s among the vertices so that their distances in T match those in D. A nice application is in evolutionary biology where the tree T aims to approximate the branching process leading to the observed distances in D [Cavalli-Sforza and Edwards 1967]. We consider the total error, that is the sum of distance errors over all pairs of points. We present a deterministic polynomial time algorithm minimizing the total error within a constant factor. We can do this both for general trees, and for the special case of ultrametrics with a root having the same distance to all vertices in s. The problems are APX-hard, so a constant factor is the best we can hope for in polynomial time. The best previous approximation factor was O((log n)(log log n) by Ailon and Charikar [2005] who wrote 'Determining whether an O(1) approximation can be obtained is a fascinating question'.
AB - We consider the numerical taxonomy problem of fitting a positive distance function D}:\binom{S2rightarrow R}> 0 by a tree metric. We want a tree T with positive edge weights and including s among the vertices so that their distances in T match those in D. A nice application is in evolutionary biology where the tree T aims to approximate the branching process leading to the observed distances in D [Cavalli-Sforza and Edwards 1967]. We consider the total error, that is the sum of distance errors over all pairs of points. We present a deterministic polynomial time algorithm minimizing the total error within a constant factor. We can do this both for general trees, and for the special case of ultrametrics with a root having the same distance to all vertices in s. The problems are APX-hard, so a constant factor is the best we can hope for in polynomial time. The best previous approximation factor was O((log n)(log log n) by Ailon and Charikar [2005] who wrote 'Determining whether an O(1) approximation can be obtained is a fascinating question'.
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U2 - 10.1109/FOCS52979.2021.00054
DO - 10.1109/FOCS52979.2021.00054
M3 - Conference contribution
AN - SCOPUS:85127156121
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 468
EP - 479
BT - Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021
PB - IEEE Computer Society
T2 - 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021
Y2 - 7 February 2022 through 10 February 2022
ER -