Research

In my previous academic research positions, I studied computation and geometry, especially their intersections.

A current list of my papers is below, partitioned by topic and in reverse chronological order.
Topics include self-assembly (tile-based and otherwise), folding, tiling, and reconfiguration.

Tile Self-Assembly

• On the Effects of Hierarchical Self-Assembly for Reducing Program-Size Complexity, with Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstate, David Furcy, Matthew J. Patitz, Robert Schweller, and Scott M. Summers.
  • Theoretical Computer Science, 894, 50-78, 2021.


• Nearly Constant Tile Complexity for any Shape in Two-Handed Tile Assembly, with Robert Schweller and Tim Wylie.
  • Algorithmica, 81, 3114-3135, 2019.


• Freezing Simulates Non-Freezing Tile Automata, with Cameron Chalk, Austin Luchsinger, Eric Martinez, Robert Schweller, and Tim Wylie.
  • Proceedings of the 24th International Conference on DNA Computing and Molecular Programming (DNA 2018), LNCS 11145, 155-172, 2018.


• Optimal Staged Self-Assembly of Linear Assemblies, with Cameron Chalk, Eric Martinez, Robert Schweller, Luis Vega, and Tim Wylie.
  • Natural Computing, 18, 527-548, 2019.
  • Proceedings of the 17th International Conference on Unconventional Computation and Natural Computation (UCNC 2018), 16-31, 2018.


• Complexities for High-Temperature Tile Self-Assembly, with Robert Schweller and Tim Wylie.
  • Proceedings of the 23rd International Conference on DNA Computing and Molecular Programming (DNA 2017), LNCS 10467, 98-109, 2017.


• Verification in Staged Tile Self-Assembly, with Robert Schweller and Tim Wylie.
  • A full version on arXiv.
  • Proceedings of 16th International Conference on Unconventional Computation and Natural Computation (UCNC 2017), 98-112, 2017.
  • Slides of a talk at UCNC 2017.


• Optimal Staged Self-Assembly of General Shapes, with Cameron Chalk, Eric Martinez, Robert Schweller, Luis Vega, and Tim Wylie.
  • Proceedings of the 24th Annual European Symposium on Algorithms (ESA), 2016.
  • Algorithmica, 80(4), 1383-1409, 2018.
  • A full version on arXiv.


• Resiliency to Multiple Nucleation in Temperature-1 Self-Assembly, with Matthew J. Patitz, Trent A. Rogers, Robert T. Schweller, and Scott M. Summers.
  • Proceedings of the 22nd International Conference on DNA Computing and Molecular Programming (DNA 2016), 98-113, 2016.


• A Brief Tour of Theoretical Tile Self-Assembly.
  • Proceedings of the 22nd International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), 26-31, 2016.
  • Slides of a talk at AUTOMATA 2016.


• The Complexity of Fixed-Height Patterned Tile Self-Assembly, with Shinnosuke Seki.
  • A full version on arXiv.
  • Proceedings of the 21st International Conference on Implementation and Application of Automata (CIAA), 248-259, 2016.
  • International Journal of Foundations of Computer Science, 28(5), 465-482, 2017.


• Size-Dependent Tile Self-Assembly: Constant-Height Rectangles and Stability, with Sándor P. Fekete and Robert T. Schweller.
  • A full version on arXiv.
  • Proceedings of the 26th International Symposium on Algorithms and Computation (ISAAC), LNCS 9472, 296-306, 2015.
  • Slides and pre-recorded video of a talk at ISAAC 2015.


• One Tile to Rule Them All: Simulating Any Tile Assembly System with a Single Universal Tile, with Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Matthew J. Patitz, Robert T. Schweller, and Damien Woods.
  • A full version on arXiv.
  • Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP), 368-379, 2014.
  • Slides of a talk at ICALP 2014.


• Size-Separable Tile Self-Assembly: A Tight Bound for Temperature-1 Mismatch-Free Systems.
  • A full version on arXiv.
  • Natural Computing, 15(1), 143-151, 2016.
  • Proceedings of Unconventional Computation and Natural Computation (UCNC 2014), 367-378, 2014.
  • Slides of a talk at UCNC 2014.


• Staged Self-Assembly and Polyomino Context-Free Grammars (Ph.D. thesis).
  • The up-to-date version with some revisions.
  • The Tufts Computer Science Department Technical Report.
  • Slides and pre-recorded video of my defense talk.


• Intrinsic Universality in Tile Self-Assembly Requires Cooperation, with Pierre-Etienne Meunier, Matthew J. Patitz, Scott M. Summers, Guillaume Theyssier, and Damien Woods.
  • A full version on arXiv.
  • Proceedings of the 25th Symposium on Discrete Algorithms (SODA), 752-771, 2014.
  • Slides and pre-recorded video of a talk at SODA 2014.


• Staged Self-Assembly and Polyomino Context-Free Grammars.
  • Natural Computing 14(2), 293-302, 2015. Also appearing as a full version on arXiv.
  • Proceedings of the 19th International Conference on DNA Computing and Molecular Programming (DNA 2013), LNCS 8141, 174-188, 2013.
  • Slides and pre-recorded video of a talk at DNA 19.


• Two Hands are Better than One (up to constant factors): Self-Assembly in the 2HAM vs. aTAM, with Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Robert T. Schweller, and Scott M. Summers.
  • A full version on arXiv.
  • Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (STACS), LIPIcs 20, 172-184, 2013.
  • Slides of a talk at Caltech.


• One-Dimensional Staged Self-Assembly, with Erik D. Demaine, Sarah Eisenstat, and Mashhood Ishaque.
  • Natural Computing 12(2), 247-258, 2013.
  • Proceedings of the 17th International Conference on DNA Computing and Molecular Programming, LNCS 8141, 100-114, 2013.
  • Slides of a talk at DNA 17.
  • Slides of my qualifying exams talk on the results.

Other Self-Assembly

• Non-Determinism Reduces Construction Time in Active Self-Assembly Using an Insertion Primitive, with Benjamin Hescott and Caleb Malchik.
  • Proceedings of the 24th International Computing and Combinatorics Conference (COCOON), 626-637, 2018.
  • Slides of a talk at COCOON 2018.


• Yield Prediction in Parallel Homogeneous Assembly, with Dhananjay Ipparthi, Metin Sitti, Marco Dorigo, and Massimo Mastrangeli.
  • Soft Matter, 13, 7595-7608, 2017.


• Design of Geometric Molecular Bonds, with David Doty.
  • IEEE Transactions on Molecular, Biological, and Multi-Scale Communications, 3(1), 13-23, 2017. Also appearing as a full version on arXiv.
  • Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT), 1789-1793, 2016.


• Dipole Codes Attractively Encode Glue Functions, with Dhananjay Ipparthi and Massimo Mastrangeli.
  • Theoretical Computer Science, 671, 19-25, 2017. Also appearing as a full version on arXiv.


• A Study of Yield Predictions for a Model of Homogeneous Self-Assembling Components, With Dhananjay Ipparthi, Massimo Mastrangeli, and Marco Dorigo.
  • Proceedings of the 1st Symposium on Swarm Behavior and Bio-Inspired Robotics (SWARM), 168-171, 2015.


• More Tight Bounds for Active Self-Assembly Using an Insertion Primitive, with Benjamin Hescott and Caleb Malchik.
  • A full version on arXiv.
  • Slides and recorded video (part 1, part 2) of a talk at LIAFA.


• Tight Bounds for Active Self-Assembly Using an Insertion Primitive, with Benjamin Hescott and Caleb Malchik.
  • Algorithmica, 77(2), 537-554, 2017. Also appearing as a full version on arXiv.
  • Proceedings of the 22nd European Symposium on Algorithms (ESA), 677-688, 2014.
  • Slides of a talk at ESA 2014.

Folding

• Vertex Unfoldings of Orthogonal Polyhedra: Positive, Negative, and Inconclusive Results, with Luis A. Garcia, Andres Gutierrez, and Isaac Ruiz.
  • Proceedings of the 30th Canadian Conference on Comptational Geometry (CCCG), 217-222, 2018.


• Polycube Unfoldings Satisfying Conway's Criterion, with Stefan Langerman.
  • An abstract version appearing at JCDCG^3 2016.
  • Print-and-cut images for unfoldings of the hat hexacube, fork hexacube, plus heptacube, divot octacube, and Dali cross octacube.


• Covering Folded Shapes, with Oswin Aichholzer, Greg Aloupis, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Michael Hoffman, Anna Lubiw, and Jack Snoeyink.
  • Journal of Computational Geometry (JoCG), 5(1), 150-168, 2014.
  • Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG), 73-78, 2013.

Tiling

• Some Open Problems in Polyomino Tilings.
  • Proceedings of 22nd International Conference on Developments in Language Theory (DLT), 74-82, 2018.


• Packing Cube Nets into Rectangles with O(1) Holes, with Erik D. Demaine, Martin L. Demaine, Ryuhei Uehara, and Yushi Uno.
  • Discrete and Computational Geometry, Graphs, and Games (JCDCGGG 2018), LNCS 13034, 152–164, 2021.
  • An abstract version appearing at JCDCG^3 2018.


• A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino, with Stefan Langerman.
  • A full version on arXiv.
  • Proceedings of the 32nd International Symposium on Computational Geometry.
  • Slides and pre-recorded video of a 16-minute talk at SOCG 2016.
  • Slides of a 45-minute talk at ETH Zurich.


• An Optimal Algorithm for Tiling the Plane with a Translated Polyomino.
  • Proceedings of the 26th International Symposium on Algorithms and Computation (ISAAC), LNCS 9472, 3-13, 2015. Also appearing as a full version on arXiv.
  • An abstract version appearing at CG Week 2015 (Young Researchers Forum).
  • Slides and pre-recorded video of a 20-minute talk at ISAAC 2015.
  • Slides and pre-recorded video of a 13-minute talk at CG Week 2015.


• A Complete Classification of Tilemakers, with Stefan Langerman.
  • An abstract version appearing at JCDCG^2 2015.
  • Slides and pre-recorded video of a talk at JCDCG^2 2015.

Reconfiguration

• Turning Around and Around: Motion Planning through Thick and Thin Turnstiles, with Aster Greenblatt, Oscar Hernandez, Robert A. Hearn, Yichao Hou, Hiro Ito, Minwoo Kang, and Aaron Williams.
  • Proceedings of the 33rd Canadian Conference on Computational Geometry (CCCG), 377-387, 2021.


• Reconfiguration of Satisfying Assignments and Subset Sums: Easy to Find, Hard to Connect, with Jean Cardinal, Erik D. Demaine, David Eppstein, and Robert A. Hearn.
  • Theoretical Computer Science, 806, 332-343, 2020. Also appearing as a full version on arXiv.
  • Proceedings of the 24th International Computing and Combinatorics Conference (COCOON), 365-377, 2018.
  • Slides of a talk at COCOON 2018.


• Algorithms for Designing Pop-up Cards, with Zachary Abel, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw, Diane L. Souvaine, and Giovanni Viglietta.
  • Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (STACS), LIPIcs 20, 269-280, 2013.


• Algorithms for Solving Rubik's Cubes, with Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, and Anna Lubiw.
  • A full version on arXiv.
  • Proceedings of the 19th European Symposium on Algorithms (ESA), LNCS 6942, 689-700, 2011.
  • MIT News, Tufts Now, and New Scientist coverage.


• Simultaneously Flippable Edges in Triangulations, with Diane L. Souvaine and Csaba Tóth.
  • Ferran Hurtado Festschrift, LNCS 7579, 138-145, 2012.
  • Proceedings of the XIV Spanish Meeting on Computational Geometry (EGC), 2011.

Visibility

• Diffuse Reflection Radius in a Simple Polygon, with Eli Fox-Epstein and Csaba D. Tóth.
  • Algorithmica, 76(4), 910-931, 2016. Also appearing as a full version on arXiv.
  • Proceedings of the 20th International Computing and Combinatorics Conference (COCOON), LNCS 8591, 239-250, 2014.
  • Slides of a talk at COCOON 2014.


• Diffuse Reflection Diameter in Simple Polygons, with Gill Barequet, Sarah M. Cannon, Eli Fox-Epstein, Benjamin Hescott, Diane L. Souvaine, and Csaba D. Tóth.
  • Discrete Applied Mathematics, 210(10), 123-132, 2016. Also appearing as a full version on arXiv.
  • Proceedings of the 7th Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS), ENDM 44, 345-350, 2013.


• Hidden Mobile Guards in Simple Polygons, with Sarah Cannon and Diane L. Souvaine.
  • A full version on arXiv.
  • Proceedings of the 24th Canadian Conference on Computational Geometry (CCCG), 161-166, 2012.
  • Proceedings of the 21st Fall Workshop on Computational Geometry (FWCG), 2011.
  • Slides of a talk at CCCG 2012.
  • Slides of a talk at FWCG 2011.


• Open Guard Edges and Edge Guards in Simple Polygons, with Csaba Tóth and Godfried T. Toussaint.
  • Ferran Hurtado Festschrift, LNCS 7579, 54-64, 2012.
  • Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG), 449-454, 2011.
  • Slides of a talk at CCCG 2011.


• Convexifying Polygons while Maintaining Internal Visibility, with Oswin Aichholzer, Greg Aloupis, Erik D. Demaine, Martin L. Demaine, Vida Dujmović, Ferran Hurtado, Anna Lubiw, Günter Rote, André Schulz, and Diane L. Souvaine.
  • Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG), 229-234, 2011.


• Face Guards for Art Galleries, with Diane L. Souvaine and Raoul Veroy.
  • Proceedings of the XIV Spanish Meeting on Computational Geometry (EGC), 2011.
  • Slides of a talk at EGC 2011.

Other Computational Geometry

• Spanning Properties of Theta-Theta-6, with Mirela Damian and John Iacono.
  • Proceedings of the 21st Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG^3), 2018.


• Inapproximability of the Smallest Superpolyomino Problem.
  • A full version on arXiv.
  • Proceedings of the 22nd Fall Workshop on Computational Geometry (FWCG), 2012.
  • Slides of a talk at FWCG 2012.


• Constrained Tri-Connected Planar Straight Line Graphs, with Mashhood Ishaque, Diane L. Souvaine, and Csaba D. Tóth.
  • Thirty Essays on Geometric Graph Theory, Algorithms and Combinatorics, Springer, 49-70, 2013.
  • Proceedings of the 20th Fall Workshop on Computational Geometry (FWCG), 2011.


• Bounded-Degree Polyhedronization of Point Sets, with Gill Barequet, Nadia Benbernou, David Charlton, Erik D. Demaine, Martin L. Demaine, Mashhood Ishaque, Anna Lubiw, André Schulz, Diane L. Souvaine, and Godfried T. Toussaint.
  • Computational Geometry 46(2), 148-153, 2013.
  • Proceedings of the 22nd Canadian Conference on Computational Geometry (CCCG), 99-102, 2010.
  • Slides of a talk at CCCG 2010.


• Connecting Obstacles in Vertex-Disjoint Paths, with Marwan Al-Jubeh, Gill Barequet, Mashhood Ishaque, Diane L. Souvaine, and Csaba D. Tóth.
  • Proceedings of the 26th European Workshop on Computational Geometry (EuroCG), 2010.

Other Topics

• Mad Science is Provably Hard: Puzzles in Hearthstone's Boomsday Lab are NP-hard, with Michael Hoffman and Jayson Lynch.
  • A full version on arXiv.
  • Journal of Information Processing, 28, 919-928, 2020.


• Virtual Cane Creation for Glassblowers, with Kimberly Baldauf, Benjamin Lee, James McCann, Erik Demaine, Martin Demaine, and Peter Houk.
  • Proceedings of SMI 2015 - ISAMA/FASE: Fabrication and Sculpting Event, Hyperseeing, 17-22, Summer 2015.
  • The VirtualGlass project webpage.


• Exploring Agent-Based Simulations in Political Science Using Aggregate Temporal Graphs, with R. Jordan Crouser, Jeremy G. Freeman, and Remco Chang.
  • Proceedings of the IEEE Pacific Symposium on Visualization, 177-184, 2013.


• Studying on the Move: Enriched Presentation Video for Mobile Devices, with Qiyam Tung, Quanfu Fan, Juhani Torkkola, Ranjini Swaminathan, Kobus Barnard, Arnon Amir, and Alon Efrat.
  • Proceedings of the 28th IEEE International Conference on Computer Communications Workshops, 1-6, 2009.