Drawing Borders Efficiently

  • Kazuo Iwama
  • Eiji Miyano
  • Hirotaka Ono
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4475)


A spreadsheet, especially MS Excel, is probably one of the most popular software applications for personal-computer users and gives us convenient and user-friendly tools for drawing tables. Using spreadsheets, we often wish to draw several vertical and horizontal black lines on selective gridlines to enhance the readability of our spreadsheet. Such situations we frequently encounter are formulated as the Border Drawing Problem (BDP). Given a layout of black line segments, we study how to draw it efficiently from an algorithmic view point, by using a set of border styles and investigate its complexity. (i) We first define a formal model based on MS Excel, under which the drawability and the efficiency of border styles are discussed, and then (ii) show that unfortunately the problem is \({\cal NP}\)-hard for the set of the Excel border styles and for any reasonable subset of the styles. Moreover, in order to provide potentially more efficient drawing, (iii) we propose a new compact set of border styles and show a necessary and sufficient condition of its drawability.


Line Segment Vertical Line Segment Horizontal Line Segment Horizontal Black Line Black Border 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Kazuo Iwama
    • 1
  • Eiji Miyano
    • 2
  • Hirotaka Ono
    • 3
  1. 1.School of Informatics, Kyoto University, Kyoto 606-8501Japan
  2. 2.Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Fukuoka 820-8502Japan
  3. 3.Department of Computer Science and Communication Engineering, Kyushu University, Fukuoka 819-0395Japan

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