## Fitting Distances by Tree Metrics Minimizing the Total Error within a Constant Factor

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

#### Standard

**Fitting Distances by Tree Metrics Minimizing the Total Error within a Constant Factor.** / Cohen-Addad, Vincent ; Das, Debarati; Kipouridis, Evangelos; Parotsidis, Nikos; Thorup, Mikkel.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

#### Harvard

*2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS).*IEEE, pp. 1-12, 62nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2021)), Virtual, 07/02/2022. https://doi.org/10.1109/FOCS52979.2021.00054

#### APA

*2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)*(pp. 1-12). IEEE. https://doi.org/10.1109/FOCS52979.2021.00054

#### Vancouver

#### Author

#### Bibtex

}

#### RIS

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

PY - 2022

Y1 - 2022

N2 - We consider the numerical taxonomy problem of fitting a positive distance function D:(S2)→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((logn)(loglogn)) 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:(S2)→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((logn)(loglogn)) by Ailon and Charikar [2005] who wrote "Determining whether an O(1) approximation can be obtained is a fascinating question".

U2 - 10.1109/FOCS52979.2021.00054

DO - 10.1109/FOCS52979.2021.00054

M3 - Article in proceedings

SP - 1

EP - 12

BT - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)

PB - IEEE

T2 - 62nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2021))

Y2 - 7 February 2022 through 11 February 2022

ER -

ID: 309113911