Geometric Algorithms for Portable devices

• Project/Area Number: 17K12635
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: Tohoku University
• Principal Investigator: Korman Matias 東北大学, 情報科学研究科, 助教 (80732718)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Discontinued (Fiscal Year 2019)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: Algorithms / Computational Geometry / Distributed algorithms / NP-completeness / Data Structures / Simple Polygons / Routing / Sensor Networks / Computer Science / Time-Space Trade-off / Combinatorial Geometry / Ad-Hoc Networks / Ad-hoc Networks / Geometric Graphs

Outline of Annual Research Achievements

Due to a change in location, we decided to interrupt the grant halfway through the year. Nonetheless, several of the milestones were achieved, even those planned for 2020 and 2021:
-Although the concept of convex hull is well known and studied, its extension to environment with obstacles was never studied. We introduced the problem, showed its complexity and introduced the first algorithm for computing it
-We studied the communication protocol for modular robots. Given a configuration of robots, we are interested in them communication so that they can reach another target shape. Although the problem turned out to be PSPACE hard (proof currently under review), we gave a constructive algorithm for the particular case in which you can add 5 helping robots in the exterior.

Research Products

• [Journal Article] Dynamic Graph Coloring (2019)
  • Author(s): Luis Barba, Jean Cardinal, Matias Korman, Stefan Langerman, Andre; van Renssen, Marcel Roeloffzen, Sander Verdonschot
  • Journal Title: Algorithmica Volume: 81(4) Issue: 4 Pages: 1319-1341
  • DOI: 10.1007/s00453-018-0473-y
• [Journal Article] Faster algorithms for growing prioritized disks and rectangles (2019)
  • Author(s): Hee-Kap Ahn, Sang Won Bae, Jong Min Choi, Matias Korman, Wolfgang Mulzer, Eunjin Oh, Ji-won Park, Ande van Renssen, Antoine Vigneron
  • Journal Title: Comput. Geom Volume: 80 Pages: 23-39
  • DOI: 10.1016/j.comgeo.2019.02.001
• [Journal Article] Packing plane spanning graphs with short edges in complete geometric graphs (2019)
  • Author(s): Oswin Aichholzer, Thomas Hackl, Matias Korman, Alexander Pilz, Andre van Renssen, Marcel Roeloffzen, Gunter Rote, Birgit Vogtenhuber
  • Journal Title: Comput. Geom Volume: 82 Pages: 1-15
  • DOI: 10.1016/j.comgeo.2019.04.001
• [Journal Article] Group evolution patterns in running races (2019)
  • Author(s): Yago Diez, Marta Fort, Matias Korman, Joan Antoni Sellares
  • Journal Title: Inf. Sci Volume: 479 Pages: 20-39
  • DOI: 10.1016/j.ins.2018.11.044
• [Journal Article] Computing the geodesic centers of a polygonal domain (2019)
  • Author(s): S. W. Bae, M. Korman, and Y. Okamoto
  • Journal Title: Computational Geometry: Theory and Applications Volume: 77 Pages: 3-9
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Gap-planar graphs (2018)
  • Author(s): S. W. Bae, J.-F. Baffier, J. Chun, P. Eades, K. Eickmeyer, L. Grilli, S.-H. Hong, M. Korman, F. Montecchiani, I. Rutter, and C. D. Toth
  • Journal Title: Theoretical Computer Science Volume: 745 Pages: 36-52
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Computational geometry column 67. (2018)
  • Author(s): B. Banyassady, M. Korman, and W. Mulzer
  • Journal Title: SIGACT News, 49 Volume: 2 Pages: 77-94
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Improved time-space trade-offs for computing voronoi diagrams (2018)
  • Author(s): B. Banyassady, M. Korman, W. Mulzer, A. v. Renssen, M. Roeloffzen, P. Seiferth, and Y. Stein
  • Journal Title: Journal of Computational Geometry Volume: 1 Pages: 191-212
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Dynamic graph coloring (2018)
  • Author(s): L.Barba, J.Cardinal, M.Korman, S.Langerman, A.v.Renssen, M.Roeloffzen,and S.Verdonschot
  • Journal Title: Algorithmica Volume: 1 Pages: 1-1
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Routing on the visibility graph (2018)
  • Author(s): P. Bose, M. Korman, A. van Renssen, and S. Verdonschot
  • Journal Title: Journal of Computational Geometry Volume: 9(1) Pages: 430-453
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] High dimensional consistent digital segments (2018)
  • Author(s): M.Chiu and M.Korman
  • Journal Title: SIAM Journal on Discrete Mathematics Volume: 32(4) Pages: 2566-2590
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Line segment covering of cells in arrangements (2018)
  • Author(s): Korman Matias、Poon Sheung-Hung、Roeloffzen Marcel
  • Journal Title: Information Processing Letters Volume: 129 Pages: 25-30
  • DOI: 10.1016/j.ipl.2017.09.002
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The dual diameter of triangulations (2018)
  • Author(s): Korman Matias、Langerman Stefan、Mulzer Wolfgang、Pilz Alexander、Saumell Maria、Vogtenhuber Birgit
  • Journal Title: Computational Geometry: Theory and Applications Volume: 68 Pages: 243-252
  • DOI: 10.1016/j.comgeo.2017.06.008
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Colored spanning graphs for set visualization (2018)
  • Author(s): Hurtado Ferran、Korman Matias、van Kreveld Marc、Loffler Maarten、Sacristan Vera、Shioura Akiyoshi、Silveira Rodrigo I.、Speckmann Bettina、Tokuyama Takeshi
  • Journal Title: Computational Geometry: Theory and Applications Volume: 68 Pages: 262-276
  • DOI: 10.1016/j.comgeo.2017.06.006
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Stabbing segments with rectilinear objects (2017)
  • Author(s): Claverol Merce、Garijo Delia、Korman Matias、Seara Carlos、Silveira Rodrigo I.
  • Journal Title: Applied Mathematics and Computation Volume: 309 Pages: 359-373
  • DOI: 10.1016/j.amc.2017.04.001
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Computing the L1 geodesic diameter and center of a polygonal domain (2017)
  • Author(s): S. W. Bae, M. Korman, J. S. B. Mitchell, Y. Okamoto, V. Polishchuk, and H. Wang. . , pages 1-28, 2016
  • Journal Title: Discrete & Computational Geometry Volume: 57(3) Issue: 3 Pages: 674-701
  • DOI: 10.1007/s00454-016-9841-z
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Jean-Lou De Carufel, Matthew J. Katz, Matias Korman, Andre; van Renssen, Marcel Roeloffzen, Shakhar Smorodinsky (2017)
  • Author(s): On interference among moving sensors and related problems
  • Journal Title: Journal of Computational Geometry Volume: 8 Pages: 32-46
  • DOI: 10.20382/JOCG.V8I1A3
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Boris Aronov, Matias Korman, Simon Pratt, Andre; van Renssen, Marcel Roeloffzen (2017)
  • Author(s): Time-space trade-offs for triangulating a simple polygon.
  • Journal Title: Journal of Computational Geometry Volume: 8 Pages: 105-124
  • DOI: 10.20382/JOCG.V8I1A6
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Hanabi is NP-hard, even for cheaters who look at their cards (2017)
  • Author(s): Baffier Jean-Francois、Chiu Man-Kwun、Diez Yago、Korman Matias、Mitsou Valia、van Renssen Andre、Roeloffzen Marcel、Uno Yushi
  • Journal Title: Theoretical Computer Science Volume: 675 Pages: 43-55
  • DOI: 10.1016/j.tcs.2017.02.024
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Computing the Geodesic Centers of a Polygonal Domain (2016)
  • Author(s): Sang Won Bae, Matias Korman, and Yoshio Okamoto
  • Journal Title: Computational Geometry: Theory and Applications Volume: 印刷中 Pages: 3-9
  • DOI: 10.1016/j.comgeo.2015.10.009
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Circumscribing Polygons and Polygonizations for Disjoint Line Segments (2019)
  • Author(s): Hugo A. Akitaya, Matias Korman, Mikhail Rudoy, Diane L. Souvaine, Csaba D. Toth
  • Organizer: SoCG 2019: 9:1-9:17
  • Int'l Joint Research
• [Presentation] Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers (2019)
  • Author(s): Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmovic, Robin Y. Flatland, Matias Korman, Belen Palop, Irene Parada, Andre van Renssen, Vera Sacristan
  • Organizer: ESA 2019: 3:1-3:14
  • Int'l Joint Research
• [Presentation] Circumscribing polygons and polygonizations for disjoint line segments. (2019)
  • Author(s): H. Akitaya, M. Korman, M. Rudoy, D. Souvaine, and C. Toth.
  • Organizer: Symposium on Computational geometry (SoCG’19)
  • Int'l Joint Research
• [Presentation] Rectilinear link diameter and radius in a rectilinear polygonal domain (2018)
  • Author(s): E. Arseneva, M. Chiu, M. Korman, A. Markovic, Y. Okamoto, A. Ooms, A. van Renssen, and M. Roeloffzen.
  • Organizer: International Symposium on Algorithms and Computation
  • Int'l Joint Research
• [Presentation] Experimental Study of Compressed Stack Algorithms in Limited Memory Environments (2018)
  • Author(s): Jean-Francois Baffier, Yago Diez, Matias Korman
  • Organizer: Symposium on Experimental Algorithms
  • Int'l Joint Research
• [Presentation] Routing in polygonal domains (2017)
  • Author(s): B. Banyassady, M. Korman, W. Mulzer, A. van Renssen, M. Roeloffzen, P. Seiferth, Y. Stein, B. Vogtenhuber, and M. Willert
  • Organizer: Proc. of the 28th International Symposium on Algorithms and Computation (ISAAC'17)
  • Int'l Joint Research
• [Presentation] Routing on the visibility graph (2017)
  • Author(s): P. Bose, M. Korman, A. van Renssen, and S. Verdonschot
  • Organizer: Proc. of the 28th International Symposium on Algorithms and Computation (ISAAC'17)
  • Int'l Joint Research
• [Presentation] Faster algorithms for growing prioritized disks and rectangles (2017)
  • Author(s): H.-K. Ahn, S. W. Bae, J. Choi, M. Korman, W. Mulzer, E. Oh, J. won Park, A. van Renssen, and A. Vigneron
  • Organizer: Proc. of the 28th International Symposium on Algorithms and Computation (ISAAC'17)
  • Int'l Joint Research
• [Presentation] Gap-planar graphs (2017)
  • Author(s): S. W. Bae, J.-F. Baffier, J. Chun, P. Eades, K. Eickmeyer, L. Grilli, S.-H. Hong, M. Korman, F. Montecchiani, I. Rutter, and C. D. Toth
  • Organizer: Proc. of the 25th International Symposium on Graph Drawing (GD'17)
  • Int'l Joint Research
• [Presentation] Constrained routing between non-visible vertices (2017)
  • Author(s): P. Bose, M. Korman, A. van Renssen, and S. Verdonschot
  • Organizer: Proc. of the 23rd International Conference on Computing and Combinatorics (COCOON'17)
  • Int'l Joint Research
• [Presentation] Balanced line separators of unit disk graphs (2017)
  • Author(s): P. Carmi, M. Chiu, M. Katz, M. Korman, Y. Okamoto, A. van Renssen, M. Roeloffzen, T. Shiitada, and S. Smorodinsky
  • Organizer: Proc. of the 16th Algorithms and Data Structures Symposium (WADS'17)
  • Int'l Joint Research
• [Presentation] Dynamic graph coloring (2017)
  • Author(s): L. Barba, J. Cardinal, M. Korman, S. Langerman, A. v. Renssen, M. Roeloffzen, and S. Verdonschot
  • Organizer: Proc. of the 16th Algorithms and Data Structures Symposium (WADS'17)
  • Int'l Joint Research
• [Presentation] High dimensional consistent digital segments (2017)
  • Author(s): M. Chiu and M. Korman
  • Organizer: Proc. of the 33rd Symposium on Computational geometry (SoCG'17)
  • Int'l Joint Research