Hot News
(11/Feb/16)
Günter Rote found a gap in the proof of the upper bound on λ
claimed below; We are working on fixing the proof...
(16/Dec/15)
λ < 4.5685
(Klarner's constant)
A new upper bound on λ (4.5685) was obtained; see
paper in EuroComb'15.
A few more tricks reduced the bound further, and it continues to go down.
(20/Nov/13)
Again, the Technion CS team, Roei Gelbhart, Alexander Goltman, Oleg Zlotnik,
and under my virtual supervision, performed very nicely,
winning this time a
bronze medal
(10th place out of 44) in the prestigious ACM/ICPC contest
(Southwestern Europe region) held in November 17, 2013 in Valencia, Spain.
(23/May/13)
λ > 4.0025
(Klarner's constant)
Closing a 10year effort, Günter Rote and I showed that the leading
decomal digit of λ (Klarner's constant, the asymptotic growth rate [or
growth constant] of site animals in the planar cubical lattice) is 4.
My Ph.D. student Mira Shalah participated in the last step of this research.
See more details
here.
(23/Nov/12)
Once again, the Technion CS team, Idan Elad, Olivier Hofman, and Mike Harris,
with its coach Noa Korner and under my virtual supervision, performed nicely,
winning this time a
bronze medal
(12th place) in the prestigious ACM/ICPC contest (Southwestern Europe
region) held in November 18, 2012 in Valencia, Spain.
(22/Nov/10)
The Technion CS team, Shahar Papini, Yaniv Sabo, and Carmi Grushko, with its
coach Kolman Vornovitsky and under my supervision, won a
gold medal
(2nd place) in the prestigious ACM/ICPC contest (Southwestern Europe
region) held in November 21, 2010 in Madrid, Spain.
(Shahar almost did not compete since he lost both his passport and his
contest badge. Worldwide efforts to restore both items were successful.)
(04/Mar/09)
The Technion awarded me the
Henri Taub prize for
academic excellence
for a few polyomino and polycuberelated works.
(The background of the picture in the above link is completely unrelated to
the things I do. 8)
Information for Prospective Graduate Students
Just want to be a CGGC student and then decide? Click
Here.
Would like to consider a thesis topic in Computational Geometry? Take my
Computational Geometry
course and send me a
message!
Here is a nice research problem for a thesis: Read
this paper (journal #26) and rethink about
the 3D case. Can it be improved to Ω(1/n³) by sharpening
the argument for the innermost cylinder?
For perspective,
here is
(completely out of context!) how Eli O'Hana was quoted in Yediot Akhronot in
an interview in May 1999.
Major Interests
Computational geometry
Graph theory and combinatorics
Discrete mathematics
Geometric and solid modeling
Geometric algorithms for medical imaging
Geometric algorithms for computer graphics


Current Research
Polyominoes and polycubes:
The running time of Jensen's Algorithm
λ (Klarner's constants) ≥ 3.9801
Redelmeier's algorithm on any lattice
Redelmeier's algorithm without the dimensionality curse
Formulas enumerating polycubes
Treelike convex polyominoes
Exact formula for DX(n,n3)
Permutations count polyominoes on twisted cylinders
Growth constant of tree polycubes
λ (Klarner's constants) ≥ 4 (!)
Object reconstruction from slices:
Geometrichashing algorithm
Contextenabled interpolation
Smooth blending of slices
Straightskeleton algorithm
Matability of polygons
Moving polygons around
Nonplanar interpolation
Multicolor interpolation
Biographic Details
Here are links to
a short résumé
and a list of publications.
My academic genealogy goes back to
Gauss, Bessel, and Weierstrass.
PostDoctoral Fellows:

Muthuganapathy Ramanathan
(March 2004  July 2006, collaborated with G. Elber and me)

Andrei Asinowski
(October 2010  September 2011)

Minati De
(May 2014  January 2015)
Graduate Students
Ph.D.:

Eyal Ackerman
(Ph.D., Computer Science, secondary advisor: R.Y. Pinter)
Counting problems for geometric structures:
Rectangulations, floorplans, and quasiplanar graphs
(dissertation;
defense held September 3, 2006;
now at Haifa University at Oranim, Israel)
M.Sc. in Sciences obtained while passing the Ph.D.candidacy exam in
the direct track, January 1, 2004

Amir Vaxman
(Ph.D., Computer Science)
General techniques for interpolation, reconstruction, and morphing of
polyhedral surfaces
(dissertation;
defense held April 3, 2011;
now at Vienna University of Technology, Austria)

Gadi Aleksandrowicz
(Ph.D., Computer Science)
Enumeration of lattice animals
(dissertation;
defense held July 17, 2011;
now at IBM Research Labs, Haifa, Israel)
M.Sc. in Sciences obtained while passing the Ph.D.candidacy exam in
the direct track, March 9, 2008
M.Sc.:

Vadim Makhervaks
(M.Sc., Mathematics, primary advisor: A. Bruckstein)
Image flows and oneliner graphical image representations
(thesis;
defense held November 5, 2002)

Daniel Brunstein
(M.Sc., Computer Science, secondary advisor: C. Gotsman)
Animating a camera for viewing a planar polygon
(thesis;
defense held June 18, 2003;
now at Intel, Haifa, Israel)

Vadim Rogol
(M.Sc., Electrical Engineering)
Maximizing the area of an axiallysymmetric polygon inscribed by a simple
polygon
(thesis;
defense held June 30, 2003;
now at General Electric, Tirat Carmel, Israel)

Micha Moffie
(M.Sc., Computer Science)
Counting polyominoes in two and three dimensions
(thesis;
defense held December 31, 2003;
now at IBM Research Labs, Haifa, Israel)

Evgeny Yakersberg
(M.Sc., Computer Science)
Morphing between geometric shapes using straightskeletonbased interpolation
(thesis;
defense held May 14, 2004;
now in Pattaya, Thailand)

Yuval Scharf
(M.Sc., Computer Science)
Covering points with a polygon
(thesis;
defense held September 27, 2004;
now in Mountain View, CA)

Aya Steiner
(M.Sc., Mathematics)
Matability of polygons
(thesis;
defense held February 28, 2005;
now in Haifa, Israel)

Alex Goryachev
(M.Sc., Computer Science)
Offset polygon and annulus placement problems
(thesis;
defense held November 16, 2005;
now at IBM Research Labs, Haifa, Israel)

Dimitry Kloper
(M.Sc., Computer Science, secondary advisor: with C. Gotsman)
Geometries and topologies of triangulations of point sets
(thesis;
defense held December 21, 2005;
now at Microsoft, Haifa, Israel)

David Hodorkovsky
(M.Sc., Mathematics)
2point site Voronoi diagrams
(thesis;
defense held December 22, 2005;
now at Imagine, Natanya, Israel)

Jonathan Naor
(M.Sc., Computer Science)
ddimensional variants of Heilbronn's triangle problem
(thesis;
defense held January 8, 2006;
now at Elbit Systems, Haifa, Israel)

Avishay Sidlesky
(M.Sc., Computer Science, secondary advisor: C. Gotsman)
Polygon reconstruction from line crosssections
(thesis;
defense held June 11, 2006)

Amir Vaxman
(M.Sc., Computer Science)
Nonlinear interpolation between slices
(thesis;
defense held November 22, 2006;
see also a Ph.D. entry)

Alina Shaikhet
(M.Sc., Computer Science)
The online Heilbronn's triangle problem in d dimensions
(thesis;
defense held June 20, 2007;
now in Ottawa, Canada)

Alik Zamansky
(M.Sc., Computer Science)
A framework for surface reconstruction of sparselysampled objects
(thesis;
defense held June 26, 2007;
now at BIRD Aerosystems, Herzlia, Israel)

Asenath Tal
(M.Sc., Computer Science)
Algorithms for Heilbronn's triangle problem
(thesis;
defense held April 19, 2009;
now at Red Bend Software, Hod HaSharon, Israel)

Shahar Tal
(M.Sc., Computer Science, The Open University)
Solving general lattice puzzles
(thesis;
defense held May 1, 2011;
now at HP, Israel)

Raeda Naamnieh
(M.Sc., Computer Science)
Fair multilabel reconstruction from crosssections
(thesis;
defense held November 7, 2013)

Abraham Stiefel
(M.Sc., Computer Science)
Motion planning in the presence of mobile obstacles
(thesis;
defense held October 26, 2015)
In progress:

Mira Shalah
(Ph.D., Computer Science)
On the growth constants of polyominoes and polycubes

Yufei Zheng
(M.Sc., Computer Science)
TBA
PubliclyAvailable Resources
My
electronic collection of human organs and digital terrains
(in polygonalslices format), and related software
My
partial surface matching and object registration software
My
polyhedral environment and database software (DCEL)
Software for
approximating the minimumvolume bounding box of a spatial point
set (with Sariel HarPeled)
Teaching
Computational Geometry (236719,
announcement):
Fall 1516,
Fall 1415,
Fall 1213,
Fall 1112,
Fall 1011,
Fall 0910 (Tufts University),
Fall 0809,
Spring 0708,
Spring 0607,
Spring 0506,
Spring 0405,
Spring 0304,
Fall 0203,
Spring 0102,
Spring 0001,
Spring 9900 (236603),
Spring 9899 (236601)
Project in Copmutational Geometry (236729):
Continuously (Technion),
Fall 9596 (TAU, project)
Discrete Algorithmic Geometry (238739):
Spring 1516,
Spring 1415,
Spring 1213,
Spring 1011,
Fall 0708 (236739),
Fall 0506 (236604),
Spring 0203 (236601)
Advanced Seminar on Geometric Computing:
Graphics:
Spring 0102 (236801)
Object reconstruction:
Fall 0607 (236801),
Spring 0405 (236801),
Spring 0304 (236801),
Spring 9596 (TAU)
Polyominoes and polycubes:
Fall 1516 (236803),
Fall 1415 (236804),
Spring 1112 (236801),
Fall 0809 (236803)
Computer Graphics 1 (234325):
Fall 0304
Introduction to System Programming (234122):
Fall 1617,
Fall 1314,
Fall 1213,
Fall 1112,
Fall 1011,
Spring 0910,
Spring 0809,
Fall 0708,
Fall 0607,
Fall 0506,
Fall 0405,
Fall 0304,
Fall 0203,
Fall 0102,
Fall 0001,
Fall 9900,
Fall 9899,
Spring 9495 (TAU),
Fall 9495 (TAU),
Spring 9394 (TAU)
Courses I Teach in the Current Semester (201617 I
תשע"ז)

Computational Geometry
(236719, Tuesday 12:3014:30, Taub ??)

Introduction to System Programming
(234122, Monday 12:3014:30, Taub ??)
 Project in Computational Geometry
(236729, continuously)
PhD and Postdoc,
CS, Tel Aviv University
(Tel Aviv, Israel, 199196)
Postdoc,
CS, Johns Hopkins University
(Baltimore, MD, 199698)
Sabbatical,
CS, Tufts University
(Medford, MA, 200910)
Office address:
Dept. of Computer Science
(New Taub bldg., fl. 4, rm. 428)
TechnionIsrael Inst. of Technology
Haifa 32000
Israel
+972 (4) 8293219
(ask Inbal below)
(center) +972 (4) 8295538
(dept.) +972 (4) 8293900
barequet@cs.technion.ac.il
http://www.cs.technion.ac.il/~barequet
CGGC administrative assistant:
Inbal Barazani
New Taub bldg., fl. 4, rm. 427
phone: +972 (4) 8294906;
fax: +972 (4) 8295538
inbalb@cs.technion.ac.il
View in and from the Technion:
The new Taub building, hosting the department of computer science:
(Click on the picture to see it full sized)



When the visibility is perfect, this is how the Hermon mountain
(60 miles [96.5 KM] from Haifa) is seen from my office:
(Click on the picture to see the full sight [Dani B., 07/01/2003],
and a new picture shot ten
years later [Mira S., 29/01/2013])


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