Michael Albert, Our people, Department of Computer Science

Owheo Building, Room 2.52
Tel +64 3 479 8586
Email michael.albert@otago.ac.nz

My background is in mathematics, particularly in algebra, combinatorics, and logic. These areas all relate to the theoretical side of computer science, specifically the study of (effective) computability, and the representation and manipulation of data.

I am particularly interested in algorithms for counting (either exactly or approximately), sampling from, or manipulating combinatorial objects. I am an enthusiastic advocate of the use of computing resources in problem solving activities of all types. The study of combinatorial games is a particularly fruitful source of such problems, and also provides illustrations of the thesis that some hard computational problems can be rendered much simpler by a suitable change of perspective.

Inaugural Professorial Lecture, 16th of April 2013, can be viewed here (237MB) or listened to here (67MB).

Staff List

Publications

Albert, M., Gudmundsson, B., & Ulfarsson, H. (2022). Collatz meets Fibonacci. Mathematics Magazine, 95(2), 130-136. doi: 10.1080/0025570X.2022.2023307

Albert, M., Jelínek, V., & Opler, M. (2021). Two examples of Wilf-collapse. Discrete Mathematics & Theoretical Computer Science, 22(2), 9. doi: 10.46298/DMTCS.5986

Albert, M., & Tannock, M. (2021). Prolific permutations. Electronic Journal of Combinatorics, 28(2), 2.2. doi: 10.37236/9966

Albert, M., & Vatter, V. (2020). How many pop-stacks does it take to sort a permutation? arXiv. Retrieved from https://arxiv.org/abs/2012.05275

Albert, M., Holmgren, C., Johansson, T., & Skerman, F. (2020). Embedding small digraphs and permutations in binary trees and split trees. Algorithmica, 82(3), 589-615. doi: 10.1007/s00453-019-00667-5

Albert, M., Bouvel, M., & Féray, V. (2020). Two first-order logics of permutations. Journal of Combinatorial Theory, Series A, 171, 105158. doi: 10.1016/j.jcta.2019.105158

Albert, M., & Li, J. (2019). Wilf-collapse in permutation classes having two basis elements of size three. Australasian Journal of Combinatorics, 73(3), 440-455.

Albert, M., & Vatter, V. (2019). An elementary proof of Bevan's Theorem on the growth of grid classes of permutations. Proceedings of the Edinburgh Mathematical Society, 62, 975-984. doi: 10.1017/S0013091519000026

Albert, M., Brignall, R., Ruškuc, N., & Vatter, V. (2019). Rationality for subclasses of 321-avoiding permutations. European Journal of Combinatorics, 78, 44-72. doi: 10.1016/j.ejc.2019.01.001

Albert, M., & Li, J. (2019). Uniquely-Wilf classes. Discrete Mathematics & Theoretical Computer Science, 21(2), 7. doi: 10.23638/DMTCS-21-2-7

Albert, M., & Tannock, M. (2019). Prolific compositions. Discrete Mathematics & Theoretical Computer Science, 21(2), 10. doi: 10.23638/DMTCS-21-2-7

Albert, M., & Tannock, M. (2019). Prolific compositions. arXiv. Retrieved from https://arxiv.org/abs/1904.05533

Alber, M. (2019, May). Wilf-equivalence and Wilf-collapse. Mathematics Seminar Series, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand. [Department Seminar].

Albert, M. H., Homberger, C., Pantone, J., Shar, N., & Vatter, V. (2018). Generating permutations with restricted containers. Journal of Combinatorial Theory, Series A, 157, 205-232. doi: 10.1016/j.jcta.2018.02.006

Ombler, F., Albert, M., & Hansen, P. (2018). How significant are "high" correlations between EQ-5D value sets? Medical Decision Making, 38(6), 635-645. doi: 10.1177/0272989x18778295

Albert, M., Atminas, A., & Brignall, R. (2017). Characterising inflations of monotone grid classes of permutations. Journal of Combinatorial Theory, Series A, 154, 444-463. doi: 10.1016/j.jcta.2017.09.004

Kennedy, E., Albert, M., & Nicholson, H. (2017). Do longus capitis and colli really stabilise the cervical spine? A study of their fascicular anatomy and peak force capabilities. Musculoskeletal Science & Practice, 32, 104-113. doi: 10.1016/j.msksp.2017.10.005

Kennedy, E., Albert, M., & Nicholson, H. (2017). The fascicular anatomy and peak force capabilities of the sternocleidomastoid muscle. Surgical & Radiologic Anatomy, 39(6), 629-645. doi: 10.1007/s00276-016-1768-9

Albert, M., Engen, M., Pantone, J., & Vatter, V. (2017). Universal layered permutations. arXiv. Retrieved from https://arxiv.org/abs/1710.04240

Ombler, F., Albert, M., & Hansen, P. (2017). The true significance of 'high' correlations between EQ-5D value sets [Economics Discussion Papers No. 1704]. Dunedin, New Zealand: School of Business, University of Otago. 20p. Retrieved from http://hdl.handle.net/10523/7247

Albert, M., & Brignall, R. (2016). 2 x 2 monotone grid classes are finitely based. Discrete Mathematics & Theoretical Computer Science, 18(2), 1. Retrieved from https://dmtcs.episciences.org/

Albert, M., & Jelínek, V. (2016). Unsplittable classes of separable permutations. Electronic Journal of Combinatorics, 23(2), P2.49. Retrieved from http://www.combinatorics.org

Albert, M., Lackner, M.-L., Lackner, M., & Vatter, V. (2016). The complexity of pattern matching for 321-avoiding skew-merged permutations. Discrete Mathematics & Theoretical Computer Science, 18(2), 11. Retrieved from https://dmtcs.episciences.org/

Albert, M., & McKague, M. (2016). Quantum vs. classical parallelism. In A. B. Deb & N. Kjærgaard (Eds.), Proceedings of the Matariki Workshop on Quantum Science. (pp. 22). Retrieved from http://quantum.otago.ac.nz/mqs2016.html

Fu, X., McCane, B., Mills, S., Albert, M., & Szymanski, L. (2016). Auto-JacoBin: Auto-encoder Jacobian binary hashing. arXiv. 17p. Retrieved from https://arxiv.org/abs/1602.08127

Fu, X., McCane, B., Mills, S., & Albert, M. (2015). NOKMeans: Non-Orthogonal K-means hashing. In D. Cremers, I. Reid, H. Saito & M.-H. Yang (Eds.), Computer Vision: 12th Asian Conference on Computer Vision 2014, revised selected papers, part 1: Lecture notes in computer science (Vol. 9003). (pp. 162-177). Cham, Switzerland: Springer. doi: 10.1007/978-3-319-16865-4_11

Albert, M. H., Ruškuc, N., & Vatter, V. (2015). Inflations of geometric grid classes of permutations. Israel Journal of Mathematics, 205(1), 73-108. doi: 10.1007/s11856-014-1098-8

Albert, M., & Bousquet-Mélou, M. (2015). Permutations sortable by two stacks in parallel and quarter plane walks. European Journal of Combinatorics, 43, 131-164. doi: 10.1016/j.ejc.2014.08.024

Albert, M., & Bouvel, M. (2015). A general theory of Wilf-equivalence for Catalan structures. Electronic Journal of Combinatorics, 22(4), P4.45.

Albert, M., Homberger, C., & Pantone, J. (2015). Equipopularity classes in the separable permutations. Electronic Journal of Combinatorics, 22(2), 2.2.

Fu, X., McCane, B., Mills, S., & Albert, M. (2015). How to select hashing bits? A direct measurement approach. Proceedings of the International Conference on Image and Vision Computing New Zealand (IVCNZ). 20. IEEE. doi: 10.1109/IVCNZ.2015.7761538

Trotman, A., Albert, M., & Burgess, B. (2015). Optimal packing in simple-family codecs. Proceedings of the International Conference on the Theory of Information Retrieval (ICTIR). (pp. 337-340). New York: ACM. doi: 10.1145/2808194.2809483

Albert, M. H., & Brignall, R. (2014). Enumerating indices of Schubert varieties defined by inclusions. Journal of Combinatorial Theory, Series A, 123(1), 154-168. doi: 10.1016/j.jcta.2013.12.003

Li, Y., Zhang, H., Huang, Z., & Albert, M. (2014). Optimal link scheduling for delay-constrained periodic traffic over unreliable wireless links. Proceedings of the Conference on Computer Communications (INFOCOM). (pp. 1465-1473). IEEE. doi: 10.1109/infocom.2014.6848081

Albert, M., & Bousquet-Mélou, M. (2014). Permutations sortable by two stacks in parallel and quarter plane walks [Extended Abstract]. Discrete Mathematics & Theoretical Computer Science, (pp. 585-596). [Abstract]

Albert, M. H., & Vatter, V. (2013). Generating and enumerating 321-avoiding and skew-merged simple permutations. Electronic Journal of Combinatorics, 20(2), P44.

Albert, M. H., Atkinson, M. D., Bouvel, M., Ruškuc, N., & Vatter, V. (2013). Geometric grid classes of permutations. Transactions of the American Mathematical Society, 365(11), 5859-5881. doi: 10.1090/S0002-9947-2013-05804-7

Fu, X., McCane, B., Albert, M., & Mills, S. (2013). Action recognition based on principal geodesic analysis. Proceedings of the 28th International Conference of Image and Vision Computing New Zealand (IVCNZ). (pp. 259-264). IEEE. doi: 10.1109/IVCNZ.2013.6727026

Albert, M. (2013, April). How to shuffle badly. University of Otago, Dunedin, New Zealand. [Inaugural Professorial Lecture].

Albert, M. (2012). Young classes of permutations. Australasian Journal of Combinatorics, 54(2), 49-58.

Albert, M. H., & Nowakowski, R. J. (2012). Lattices of games. Order, 29(1), 75-84. doi: 10.1007/s11083-011-9198-0

Albert, M. H., Atkinson, M. D., & Brignall, R. (2012). The enumeration of three pattern classes using monotone grid classes. Electronic Journal of Combinatorics, 19(3), P20.

Zhang, H., Albert, M., & Willig, A. (2012). Combining TDMA with Slotted Aloha for delay constrained traffic over lossy links. Proceedings of the 12th International Conference on Control Automation Robotics & Vision (ICARCV). (pp. 701-706). IEEE. doi: 10.1109/ICARCV.2012.6485243

Albert, M. H., Atkinson, M. D., & Vatter, V. (2011). Subclasses of the separable permutations. Bulletin of the London Mathematical Society, 43(5), 859-870. doi: 10.1112/blms/bdr022

Albert, M. H., Atkinson, M. D., Bouvel, M., Claesson, A., & Dukes, M. (2011). On the inverse image of pattern classes under bubble sort. Journal of Combinatorics, 2(2), 231-243.

Albert, M. H., Linton, S., Ruškuc, N., Vatter, V., & Waton, S. (2011). On convex permutations. Discrete Mathematics, 311(8-9), 715-722. doi: 10.1016/j.disc.2011.01.009

Albert, M., Cordón-Franco, A., van Ditmarsch, H., Fernández-Duque, D., Joosten, J. J., & Soler-Toscano, F. (2011). Secure communication of local states in interpreted systems. In A. Abraham, J. M. Corchado, S. Rodríguez González & J. F. De Paz Santana (Eds.), International Symposium on Distributed Computing and Artificial Intelligence: Advances in Intelligent and Soft Computing (Vol. 91). (pp. 117-124). Berlin, Germany: Springer. doi: 10.1007/978-3-642-19934-9

Albert, M. H., Atkinson, M. D., Brignall, R., Ruškuc, N., Smith, R., & West, J. (2010). Growth rates for subclasses of Av(321). Electronic Journal of Combinatorics, 17(1), R141.

Albert, M., Atkinson, M., & Linton, S. (2010). Permutations generated by stacks and deques. Annals of Combinatorics, 14(1), 3-16. doi: 10.1007/s00026-010-0042-9

Curry, B. W., Trotman, A., & Albert, M. (2010). Extricating meaning from Wikimedia article archives. Proceedings of the 15th Australasian Document Computing Symposium (ADCS). Retrieved from http://www.cs.rmit.edu.au/adcs2010/proceedings/

Albert, M. (2010). Young classes of permutations [Technical Report OUCS-2010-03]. Dunedin, New Zealand: Computer Science Department, University of Otago. 9p.

Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Handley, C. C., Holton, D. A., McCaughan, D. J., & Sagan, B. E. (2009). Monotonic sequence games. In M. H. Albert & R. J. Nowakowski (Eds.), Games of no chance 3. (pp. 309-328). Cambridge University Press.

Albert, M. H., & Linton, S. A. (2009). Growing at a perfect speed. Combinatorics, Probability & Computing, 18(3), 301-308. doi: 10.1017/s0963548309009699

Albert, M. H., Atkinson, M. D., & Vatter, V. (2009). Counting 1324, 4231-avoiding permutations. Electronic Journal of Combinatorics, 16, R136.

McCane, B., & Albert, M. (2008). Distance functions for categorical and mixed variables. Pattern Recognition Letters, 29(7), 986-993. doi: 10.1016/j.patrec.2008.01.021

Albert, M. H. (2007). On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation. Random Structures & Algorithms, 31(2), 227-238.

Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Van Ditmarsch, H. P., Handley, C. C., Holton, D. A., McCaughan, D. J., & Monteith, C. W. (2007). Cyclically closed pattern classes of permutations. Australasian Journal of Combinatorics, 38, 87-100.

Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Van Ditmarsch, H. P., Handley, C. C., Holton, D. A., & McCaughan, D. J. (2007). Compositions of pattern restricted sets of permutations. Australasian Journal of Combinatorics, 37, 43-56.

Albert, M. H., Atkinson, M. D., & Brignall, R. (2007). Permutation classes of polynomial growth. Annals of Combinatorics, 11(3 - 4), 249-264. doi: 10.1007/s00026-007-0318-x

Albert, M. H., Atkinson, M. D., Nussbaum, D., Sack, J. R., & Santoro, N. (2007). On the longest increasing subsequence of a circular list. Information Processing Letters, 101, 55-59. doi: 10.1016/j.ipl.2006.08.003

Albert, M. H., Coleman, M., Flynn, R., & Leader, I. (2007). Permutations containing many patterns. Annals of Combinatorics, 11(3 - 4), 265-270. doi: 10.1007/s00026-007-0319-9

Albert, M. H., Elder, M., Rechnitzer, A., Westcott, P., & Zabrocki, M. (2006). On the Stanley-Wilf limit of 4231-avoiding permutations and a conjecture of Arratia. Advances in Applied Mathematics, 36(2), 96-105.

Albert, M. H., Atkinson, M. D., & Brignall, R. (2006). Permutation classes of polynominal growth [Technical Report OUCS-2006-05]. Dunedin, New Zealand: Computer Science Department, University of Otago. 17p.

Albert, M. H., Atkinson, M. D., Handley, C. C., Aldred, R. E. L., McCaughan, D. J., & Sagan, B. E. (2006). Monotonic sequence games [Technical Report OUCS-2006-04]. Dunedin, New Zealand: Computer Science Department, University of Otago. 20p.

Albert, M. H., Coleman, M., Flynn, R., & Leader, I. (2006). Permutations containing many patterns [Technical Report OUCS-2006-09]. Dunedin, New Zealand: Computer Science Department, University of Otago. 6p.

Albert, M. H., & Atkinson, M. D. (2005). Simple permutations and pattern restricted permutations. Discrete Mathematics, 300, 1-15.

Albert, M. H., & Paterson, M. S. (2005). Bounds for the growth rate of meander numbers. Journal of Combinatorial Theory, Series A, 112, 250-262.

Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Handley, C. C., Holton, D. A., McCaughan, D. J., & van Ditmarsch, H. (2005). Sorting classes. Electronic Journal of Combinatorics, 12(1). Retrieved from http://www.combinatorics.org/

Albert, M. H., Aldred, R. E. L., Atkinson, M. D., van Ditmarsch, H. P., & Handley, C. C. (2005). Safe communication for card players by combinatorial designs for two-step protocols. Australasian Journal of Combinatorics, 33, 33-46.

Albert, M. H., Linton, S. J., & Ruškuc, N. (2005). The insertion encoding of permutations. Electronic Journal of Combinatorics, 12. Retrieved from http://www.combinatorics.org/Volume_12/PDF/v12i1r47.pdf

Albert, M. H., & Nowakowski, R. J. (2004). Nim restrictions. Integers, 4. Retrieved from http://www.integers-ejcnt.org/vol4.html

Albert, M. H., Aldred, R. E. L., Atkinson, M. D., van Ditmarsch, H. P., Handley, C. C., & Holton, D. A. (2004). Restricted permutations and queue jumping [Note]. Discrete Mathematics, 287, 129-133.

Albert, M. H., Golynski, A., Hamel, A. M., López-Ortiz, A., Rao, S. S., & Safari, M. A. (2004). Longest increasing subsequences in sliding windows [Note]. Theoretical Computer Science, 321, 405-414.

Albert, M. H., & Atkinson, M. D. (2003). Sorting with a forklift. Electronic Journal of Combinatorics, 9(2), 1-23. Retrieved from http://www.combinatorics.org/Volume_9/PDF/v9i2r9.pdf

Albert, M. H., Aldred, R. E., Atkinson, M. D., van Ditmarsch, H. P., Handley, B. D., & Handley, C. C. (2003). Longest subsequences in permutations. Australasian Journal of Combinatorics, 28, 225-238.

Albert, M. H., Atkinson, M. D., & Klazar, M. (2003). The enumeration of simple permutations. Journal of Integer Sequences, 6(4), 1-18. Retrieved from http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Albert/albert.pdf

Albert, M. H., Atkinson, M. D., & Ruskuc, N. (2003). Regular closed sets of permutations. Theoretical Computer Science, 306, 85-100.

Albert, M. H., Le, H., & Small, C. G. (2003). Assessing landmark influence on shape variation. Biometrika, 90(3), 669-678.

Albert, M. H., Atkinson, M. D., Handley, C. C., Holton, D., & Stromquist, W. (2002). On packing densities of permutations. Electronic Journal of Combinatorics, 9(1). Retrieved from http://www.combinatorics.org/

Albert, M. H., & Atkinson, M. D. (2002). Sorting with a fork lift. In M. Penttonen & E. Meineche Schmidt (Eds.), Proceedings of Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science. 2368, (pp. 368-377). Berlin: Springer-Verlag. [Abstract]

Albert, M. H., & Nowakowski, R. J. (2001). The game of End-Nim. Electronic Journal of Combinatorics, 8(2), 12 pages. Retrieved from www.combinatronics.org/volume_8/v8i2toc.html

Albert, M. H., Aldred, R. E., Atkinson, M. D., Handley, C. C., & Holton, D. (2001). Permutations of a multiset avoiding permutations of length 3. European Journal of Combinatorics, 22, 1021-1031.

Albert, M. H., Aldred, R. E., Holton, D., & Sheehan, J. (2001). On 3*-connected graphs. Australasian Journal of Combinatorics, 24, 193-207.

Albert, M. H., Holton, D., & Nowakowski, R. J. (2001). The ultimate categorical matching in a graph. Discrete Mathematics, 232, 1-10.

Albert, M. H., Aldred, R. E., Atkinson, M. D., & Holton, D. (2001). Algorithms for pattern involvement in permutations. In P. Eades & T. Takaoka (Eds.), Algorithms and Computation: The Proceedings of the 12th International Symposium, ISAAC 2001. (pp. 355-366). Christchurch: Springer-Verlag. [Full Paper]

Albert, M. H., & Chowdhury, A. (1999). The rationals have an AZ-Enumeration. Journal of the London Mathematical Society, 59(2), 385-395.

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