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UID:024c7f42-d879-4fdc-9c35-e386e6c0f083
X-WR-CALNAME:GT AlgoDist\, «Trajectory visibility at first sight»\, Hussein
  Kazemi
X-WR-TIMEZONE:Europe/Paris
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TZID:Europe/Paris
TZUNTIL:20271031T010000Z
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DTSTART:20251026T030000
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RDATE:20261025T030000
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DTSTAMP:20260404T120451Z
CLASS:PUBLIC
DESCRIPTION:Hussein Kazemi (LaBRI)\n\nTitle: Trajectory visibility at first
  sight\n\nAbstract:\n\nLet P be a simple polygon with n vertices\, and let
  two moving entities q(t) and r(t) travel at constant (possibly distinct) 
 speeds vq and vr along line-segment trajectories τq and τr inside P. We st
 udy the exact first-visibility time t∗= min t≥0: q(t) r(t) ⊆P\, the earlie
 st moment at which the segment joining q(t) and r(t) lies entirely within 
 P.\n\nPrior work by Eades et al. focused on this question in the setting o
 f a simple polygon. They gave a one-shot decision algorithm running in O(n
 ) time. For a stationary entity and a moving one\, they suggested a struct
 ure that\, after O(n log n) pre-processing\, answers the decision query in
  O(log n) time\, requiring O(n) space. In addition\, for moving entities\,
  after preprocessing time of O(n log⁵ n)\, they construct a data structure
  with O(n^{3/4} log³ n) query time and O(n log⁵ n) space. Variants for pol
 ygonal domains with holes or when entities cross the boundary of P lie bey
 ond our scope.\n\nIn this work\, we go beyond the decision to compute t* e
 xactly under three models for a simple polygon P. When both trajectories a
 re known in advance\, we preprocess P in O(n) time and space and thereafte
 r answer each query in O(log n) time. If one trajectory τr is fixed while 
 τq is given as query\, we build a structure in O(n log n) time and space t
 hat computes t∗in O(log² n) time per query. In a setting where the traject
 ories are not known in advance\, we develop a randomized structure with O(
 n^{1+ε}) expected pre-processing time and O(n) space\, achieving an O(√n p
 olylog(n)) expected query time for any fixed ε > 0.\n\n\n\n\n\nhttps://alg
 odist.labri.fr/index.php/Main/GT\n\nImport automatique depuis https://webm
 el.u-bordeaux.fr/home/bf-labri.ca@u-bordeaux.fr/gt.algo-dist.ics par sync_
 icals_to_drupal.py pour gt-algodist
DTSTART;TZID=Europe/Paris:20251215T110000
DTEND;TZID=Europe/Paris:20251215T120000
LOCATION:LaBRI 178
SEQUENCE:0
SUMMARY:GT AlgoDist\, «Trajectory visibility at first sight»\, Hussein Kaze
 mi
TRANSP:OPAQUE
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