Geometric Algorithms for Portable devices

2019 Fiscal Year Annual Research Report

• Project/Area Number: 17K12635
• 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
• Keywords: Algorithms / Computational Geometry / Distributed algorithms / NP-completeness

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) Pages: 1319-1341
  • DOI: https://doi.org/10.1007/s00453-018-0473-y
• [Journal Article] Computing the geodesic centers of a polygonal domain (2019)
  • Author(s): Sang Won Bae, Matias Korman, Yoshio Okamoto
  • Journal Title: Comput. Geom Volume: 77 Pages: 3-9
  • DOI: https://doi.org/10.1016/j.comgeo.2015.10.009
• [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: https://doi.org/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: https://doi.org/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: https://doi.org/10.1016/j.ins.2018.11.044
• [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