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DTSTART:20181028T020000
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DTSTART:20180323T020000
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UID:calendar.58255.field_date.0@mathematics.huji.ac.il
DTSTAMP:20210309T040403Z
CREATED:20180530T230001Z
DESCRIPTION:Date: \n\n9:00am to 9:50am\n\n\nSee also: HD-Combinatorics\,
Seminars\, Events & SeminarsLocation: \n\nFeldman Building\, Givat Ram\n\n
\n\nComputing R=P.Q \,the product of two mXm Boolean matrices [BMM] is an
ingredient\nof many combinatorial algorithms. \nMany efforts were made to
speed it beyond the standard m^3 steps\, without using\nthe algebraic mult
iplication.\nTo divide the computation task\, encoding of the rows and col
umn indices were\nused (1.1) j by (j1\,j2) k by (k1\,k2)\ne.g. using integ
er p j2=j mod p \,j1=ceiling of j/p.\nClearly\, the product of the ranges
of the digits= m1.m2 - is approximately m. \n L.Lee’s article reduced BMM
to parsing substrings of a fixed string u with\nrespect to a context-free
grammar G. But the cubic complexity persisted. \n The reduction here is to
a family of bi-graphs bunches\, each consisting of\ndirected graphs. The
family is obtained from r distinct encodings (1.1) of\nthe indices - and i
nvoking the Chinese remainder theorem to produce the BMM R=P.Q.\n If r is
an integer\, e=1/r \,m2=m^(e) then the total number of steps is\n2r.m^(2+e
). E.g. if r=10 it is 20m^(2.1).\n This almost optimal BMM [and simple ext
ensions] replaces the recourse to\ncomplicated algebraic matrix multiplica
tions . It renders its improved\ncomplexity to graph property tests which
include BMM as a sub-routine: Finding \nall edges which belong to triangle
s in a graph\, using it to reduce complexity\nof existence of k-cliques\,
or edges in 4 vertex diamonds and some other\nsemi-cliques\; Finding all p
airs shortest walks in a graph and other applications: \nUsing Valiant’s r
eduction of context-free parsing to \nBMM\, the complexity exponent three
in standard parsing is reduced to 2+e with small e.
DTSTART;TZID=Asia/Jerusalem:20180604T090000
DTEND;TZID=Asia/Jerusalem:20180604T095000
LAST-MODIFIED:20191104T060007Z
SUMMARY:HD-Combinatorics: Eli Shamir\, 'Almost optimal Boolean matrix multi
plication[BMM] - By Multi-encoding of rows and columns'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/hd-combinatorics-eli-sham
ir-almost-optimal-boolean-matrix-multiplicationbmm-multi-encoding
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