Drawing borders efficiently

Kazuo Iwama, Eiji Miyano, Hirotaka Ono

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 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.

Original languageEnglish
Title of host publicationFun with Algorithms - 4th International Conference, FUN 2007, Proceedings
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783540729136
Publication statusPublished - 2007
Event4th International Conference on Fun with Algorithms, FUN 2007 - Castiglioncello, Italy
Duration: Jun 3 2007Jun 5 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4475 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other4th International Conference on Fun with Algorithms, FUN 2007

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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