cell:
home:
(514) 294-4924
(705) 726-9954
Aaron Williams
www.math.mcgill.ca/haron
haron@uvic.ca
Research
Postdoctoral Positions
• Postdoctoral fellow at McGill University, September 2011 – September 2013, supervised by
Bruce Shepherd, Department of Mathematics and Statistics.
• Postdoctoral fellow at Carleton University, May 2010 – August 2011, supervised by Brett
Stevens, School of Mathematics and Statistics.
• Postdoctoral fellow at the University of Guelph, Winter 2010 and Fall 2013, supervised by
Joe Sawada, School of Computer Science.
Degrees
• PhD in Computer Science, supervised by Frank Ruskey and Wendy Myrvold, University of
Victoria, 2004-2009. Thesis Shift Gray Codes in Gray codes and combinatorial generation.
• Masters of Mathematics in Combinatorics & Optimization, supervised by Bertrand Guenin,
University of Waterloo, 2002-2003. Thesis Packing Directed Joins in graph theory and combinatorial optimization.
• Bachelor of Mathematics in Combinatorics & Optimization, University of Waterloo, 19962001. Graduated with distinction in Honors co-op program.
• Bachelor of Mathematics in Computer Science, University of Waterloo, 1996-2001. Graduated
with distinction in Honors co-op program.
Distinctions, Awards, and Funding
• Institut des Sciences Matématiques Undergraduate Summer Scholarship ($5,000) in 2012.
This award funded the summer research of Xi Sisi Shen that I supervised at McGill University.
• Research Grant from the Office of Naval Research in 2012 ($40,000) obtained with Bruce
Shepherd at McGill University.
• Finalist for the Distinguished Dissertation Award from the Canadian Association of Graduate
Studies in 2009. This award is for “unusually significant and original contributions to their
academic field” during the calendar year. Each Canadian university nominates one finalist
per year for the combined area of engineering, medical sciences and natural sciences.
• Finalist for the University of Victoria’s Governor General’s Gold Medal in 2009. Each faculty
nominates one finalist per year.
• Finalist for Bell Canada 125th Anniversary Scholarship in 2005. This scholarship was open
to all Canadian graduate students.
• Best paper by a PhD student, CATS 2008: The Australasian Theory Symposium, 2008 ($500)
for the paper Generating Balanced Parentheses and Binary Trees by Prefix Shifts.
• NSERC Post-Graduate Doctoral Scholarship, 2005-2008 ($63,000). This award funded my
PhD at the University of Victoria.
• Ontario Graduate Scholarship, 2002-2004 ($30,000). This award funded my Masters degree
at the University of Waterloo.
Teaching Experience
• McGill University, Instructor for COMP 252 (Honours Algorithms and Data Structures),
Winter 2012. Two lectures per week with 29 students.
• Carleton University, Instructor for Math 4805 / Math 5605 / Comp 4805 (Finite Automata),
Fall 2010. Three lectures per week with 7 students.
• University of Victoria, Instructor for CSC 322 (Logic and Computer Science), Fall 2007. Three
lectures per week with 25 students.
• University of Waterloo, Instructor for Math 135 (Classical Algebra), Fall 2003. Three lectures
per week with 60 students.
• Outstanding Teaching Assistant Award, Department of Combinatorics & Optimization, University of Waterloo, Fall 2002.
Supervising Experience
• I supervised the summer research program of Xi Sisi Shen at McGill University in 2012 and
2013. Sisi was a student in my COMP 252 course who asked if we could work together. Our
results were published at the LAGOS 2013 conference, and a journal version of our work is in
preparation. Sisi gave an excellent presentation at CanaDAM 2013, and will speak at the Joint
Mathematics Meeting in 2014. Sisi is now pursuing graduate school at Columbia University.
Academic Service
• Co-organizer of the Gray Codes and Universal Cycles mini-symposium at CanaDAM 2013.
• Organizer of the Discrete Math and Optimization seminar at McGill University, 2011–2013.
Programming and Software Development
• Programming competency in Python, C, HTML, CSS, Javascript, PostScript, and Matlab.
• Discreet Logic. Programmer and Designer, including development of internal programming
language using Lex and Yacc, Summer 1999 and Summer 2000.
• Corel Corporation. Programmer and Quality Assurance. Winter/Fall 1997, and Summer 1998.
References
•
•
•
•
Frank Ruskey, Computer Science, University of Victoria, ruskey@cs.uvic.ca.
Joe Sawada, Computer Science, University of Guelph, jsawada@uoguelph.ca.
Bruce Shepherd, Mathematics and Statistics, McGill University, bruce.shepherd@mcgill.ca.
Ron Graham, Computer Science and Engineering, University of California San Diego,
graham@ucsd.edu.
• Brett Stevens, Mathematics and Statistics, Carleton University, brett@math.carleton.ca.
• Wendy Myrvold, Computer Science, University of Victoria, wendym@cs.uvic.ca.
Publications and Submissions
Submitted to Journal
[32] J. Sawada, and A. Williams, Greedily Flipping Pancakes and Burnt Pancakes, Journal of
Discrete Applied Mathematics (submitted).
[31] A. Williams, Hamiltonicity of the Directed Cayley Graph on the Symmetric Group with Generators (1 2) and (1 2 · · · n), Journal of the American Mathematical Society (submitted).
Preprint is available on arXiv: http://arxiv.org/abs/1307.2549.
[30] W. Myrvold, A. Williams, and L. Panjer, Graceful Forests and a Parity Constraint for the
Graceful Tree Conjecture, Journal of Graph Theory (submitted).
[29] J. Sawada, A. Williams, and D. Wong, The Lexicographically Smallest Universal Cycle for
Binary Strings with Minimum Specified Weight, Journal of Discrete Algorithms (submitted).
Published Journal Articles
[28] B. Stevens and A. Williams, The Coolest Way to Generate Binary Strings, Theory of Computing Systems DOI: 10.1007/s00224-013-9486-8 (published online July 2013).
[27] J. Sawada and A. Williams, A Gray Code for Fixed-Density Necklaces and Lyndon Words in
Constant Amortized Time, Theoretical Computer Science 502 (2013) 46–54.
[26] S. Durocher, B.P. Li, D. Mondal, F. Ruskey, and A. Williams, Cool-lex Order and k-ary
Catalan Structures, Journal of Discrete Algorithms 16 (2012) 287–307.
[25] B. Stevens and A. Williams, Hamilton Cycles in Restricted and Incomplete Rotator Graphs,
Journal of Graph Algorithms and Applications 16, 4 (2012) 785–810.
[24] F. Ruskey, J. Sawada, and A. Williams, De Bruijn Sequences for Fixed-Weight Binary Strings,
SIAM Journal of Discrete Mathematics 26 2 (2012) 605–617.
[23] J. Sawada and A. Williams, Efficient Oracles for Generating Binary Bubble Languages, Electronic Journal of Combinatorics 19 1 (2012) Paper 42.
[22] F. Ruskey, J. Sawada, and A. Williams, Binary Bubble Languages and Cool-lex Order, Journal
of Combinatorial Theory Series A 119 1 (2012) 155-169.
[21] A. Holroyd, F. Ruskey, and A. Williams, Shorthand Universal Cycles for Permutations,
Algorithmica 64, 2 (2012) 215–245.
[20] F. Ruskey, and A. Williams, The Feline Josephus Problem, Theory of Computing Systems 50
1 (2012) 20-34.
[19] F. Ruskey and A. Williams, An Explicit Universal Cycle for the (n−1)-Permutations of an
n-Set, ACM Transactions on Algorithms 6 3 (2010) article 45.
[18] F. Ruskey and A. Williams, The Coolest Way to Generate Combinations, Discrete Mathematics 309 17 (2009) 5305-5320.
Published Refereed Conference Proceedings
[17] J. Sawada, A. Williams, and D. Wong, Universal cycles for weight-range binary strings, the
24th International Workshop on Combinatorial Algorithms (IWOCA 2013), Rouen, France,
Lecture Notes in Computer Science 8288 (2013) 388-399.
[16] A. Williams The Greedy Gray Code Algorithm. Workshop on Algorithms and Data Structures
(WADS 2013), London, Canada, Lecture Notes in Computer Science 8037 (2013) 525–536.
[15] X. S. Shen and A. Williams, A ‘Hot Potato’ Gray Code for Permutations, Latin Conference
on Graphs and Algorithms (LAGOS 2013), Playa del Carmen, Mexico, Electronic Notes in
Discrete Mathematics 45 (2013) 89–94.
[14] A. Williams and J. Sawada, Greedy Pancake Flipping, Latin Conference on Graphs and Algorithms (LAGOS 2013), Playa del Carmen, Mexico, Electronic Notes in Discrete Mathematics
45 (2013) 357–362.
[13] B. Stevens and A. Williams, The Coolest Order of Binary Strings, the 6th International Conference on Fun with Algorithms (FUN 2012), San Servolo, Italy, Lecture Notes in Computer
Science 7288 (2012) 322–333.
[12] B. Stevens and A. Williams, Hamilton Cycles in Restricted Rotator Graphs, the 22nd International Workshop on Combinatorial Algorithms (IWOCA 2011), Victoria, Canada, Lecture
Notes in Computer Science 7056 (2011) 324–336.
[11] S. Durocher, P. C. Li, D. Mondal, and A. Williams, Ranking and Loopless Generation of k-ary
Dyck Words in Cool-lex Order, the 22nd International Workshop on Combinatorial Algorithms
(IWOCA 2011), Victoria, Canada, Lecture Notes in Computer Science 7056 (2011) 182-194.
[10] J. Sawada, B. Stevens, and A. Williams, De Bruijn Sequences for Binary Strings with Maximum Density, the 5th Workshop on Algorithms and Computation (WALCOM 2011), New
Dehli, India, Lecture Notes in Computer Science 6552 (2011) 182-190.
[9] A. Holroyd, F. Ruskey, and A. Williams, Faster Generation of Shorthand Universal Cycles for
Permutations, the 16th International Computing and Combinatorics Conference (COCOON
2010), Nha Trang, Vietnam, Lecture Notes in Computer Science 6196 (2010) 298-307.
[8] A. Williams, O(1)-Time Unsorting by Prefix-Reversals in a Boustrophedon Linked List, the 5th
International Conference on FUN with Algorithms (FUN 2010), Ischia Island, Italy, Lecture
Notes in Computer Science 6099 (2010) 368-379.
[7] F. Ruskey and A. Williams, The Feline Josephus Problem, the 5th International Conference
on FUN with Algorithms (FUN 2010), Ischia Island, Italy, Lecture Notes in Computer Science
6099 (2010) 343-354.
[6] A. Williams, Loopless Generation of Multiset Permutations using a Constant Number of Variables by Prefix Shifts. ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), New
York, United States, SODA Proceedings (2009) 987–996.
[5] F. Ruskey and A. Williams, Generating Balanced Parentheses and Binary Trees by Prefix
Shifts, the 14th Computing: The Australasian Theory Symposium (CATS 2008), Wollongong,
Australia, Theory of Computing, 77 (2008) 107–115.
[4] G. Lee, F. Ruskey, and A. Williams, Hamming Distance from Irreducible Polynomials over
F2 , International Conference on Analysis of Algorithms (AofA 2007), Juan-les-pins, France,
Discrete Mathematics and Theoretical Computer Science AH (2007) 169–180.
[3] O. Lee and A. Williams, Packing Dicycle Covers in Planar Graphs with no K5 − e Minor, the
7th Latin American Symposium on Theoretical Informatics (LATIN 2006), Valdivia, Chile,
Lecture Notes in Computer Science 3887 (2006) 677–688.
[2] F. Ruskey and A. Williams, Generating Combinations by Prefix Shifts, the 11th International
Computing and Combinatorics Conference (COCOON 2005), Kunming, China, Lecture Notes
in Computer Science 3595 (2005) 570–576.
[1] B. Guenin and A. Williams, Advances in Packing Directed Joins, the 2nd Brazilian Symposium
on Graphs, Algorithms, and Combinatorics (GRACO 2005), Angra dos Reis, Brazil, Electronic
Notes in Discrete Mathematics 19 (2005) 249–255.
Acknowledged Contributions
• T. E. Baker and C. B. Holroyd. The topographical N170: Electrophysiological evidence of a
neural mechanism for human spatial navigation. Biological Psychology 94 (2013) 90–105.