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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240521T150000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/graphs-and-m
 atroids-massimo-vicenzo
SUMMARY:Graphs and Matroids - Massimo Vicenzo
CLASS:PUBLIC
DESCRIPTION:TITLE: Reconstructing Shredded Random Matrices\n\nSPEAKER:\n M
 assimo Vicenzo\n\nAFFILIATION:\n University of Waterloo\n\nLOCATION:\n MC 
 5479\n\nABSTRACT: The Graph Reconstruction Conjecture states that if we a
 re\ngiven the set of vertex-deleted subgraphs of some graph\, then there i
 s\na unique graph G that can be reconstructed from them. This conjecture\n
 has been open since the 60s\, and has only been solved for certain\nclasse
 s of graphs with not much progress towards the general case. We\ninstead s
 tudy adjacent reconstruction problems\, for example\, studying\nmatrices i
 nstead of graphs:  Given some binary matrix M\, suppose we\nare presented
  with the collection of its rows and columns in\nindependent arbitrary ord
 erings. From this information\, are we able to\nrecover the original matri
 x and will it be unique? We present an\nalgorithm that identifies whether 
 there is a unique ordering\nassociated with a set of rows and columns\, an
 d outputs either the\nunique correct orderings for the rows and columns or
  the full\ncollection of all valid orderings and valid matrices. We show t
 hat for\nmatrices with entries that are i.i.d. Bernoulli(p)\, that for p\n
 >2log(n)/n that the matrix is indeed unique with high probability.\nThis i
 s a joint work with Caelan Atamanchuk and Luc Devroye.
DTSTAMP:20260404T153303Z
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