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SUMMARY:Zhengchao Wan (The Ohio State University)
DTSTART:20211012T200000Z
DTEND:20211012T210000Z
DTSTAMP:20260423T021706Z
UID:TDGA/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TDGA/2/">The
  Gromov-Hausdorff distance between ultrametric spaces</a>\nby Zhengchao Wa
 n (The Ohio State University) as part of Topology\, Geometry\, & Data Anal
 ysis (TGDA) Seminar\n\n\nAbstract\nThe Gromov-Hausdorff distance $(d_GH)$ 
 is a natural distance between metric spaces. However\, computing $d_GH$ is
  NP-hard\, even in the case of finite ultrametric spaces. We identify a on
 e parameter family $\\{d_{GH\,p}\\}_{p\\in[1\,\\infty]}$ of Gromov-Hausdor
 ff type distances on the collection of ultrametric spaces such that $d_{GH
 \,1}=d_{GH}$. The extreme case when $p=\\infty$\, which we also denote by 
 $u_{GH}$\, turns out to be an ultrametric on the collection of ultrametric
  spaces. We discuss various geometric and topological properties of $d_{GH
 \,p}$ as well as some of its structural results. These structural results 
 in turn allow us to study the computational aspects of the distance. In pa
 rticular\, we establish that (1) $u_{GH}$ is computationally tractable and
  (2) when $p < \\infty$\, although $d_{GH\,p}$ is NP-hard to compute\, we 
 identify a fixed-parameter tractable algorithm for computing the exact val
 ue of $d_{GH\,p}$ between finite ultrametric spaces.\n
LOCATION:https://researchseminars.org/talk/TDGA/2/
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