https://scholars.lib.ntu.edu.tw/handle/123456789/342598
Title: | Many-to-One Boundary Labeling | Authors: | Lin, Chun-Cheng Kao, Hao-Jen HSU-CHUN YEN |
Issue Date: | Jan-2008 | Journal Volume: | 12 | Journal Issue: | 3 | Start page/Pages: | 319-356 | Source: | Journal of Graph Algorithms and Applications | Abstract: | In boundary labeling, each point site is uniquely connected to a label placed on the boundary of an enclosing rectangle by a leader, which may be a rectilinear or straight line segment. To our knowledge, all the results reported in the literature for boundary labeling deal with the so-called one-to-one boundary labeling, i.e., different sites are labelled differently. In certain applications of boundary labeling, however, more than one site may be required to be connected to a common label. In this case, the presence of crossings among leaders often becomes inevitable. Minimiz- ing the total number of crossings in boundary labeling becomes a critical design issue as crossing is often regarded as the main source of confu- sion in visualization. In this paper, we consider the crossing minimiza- tion problem for multi-site-to-one-label boundary labeling, i.e., finding the placements of labels and leaders such that the total number of crossings among leaders is minimized. We show the crossing minimization problem to be NP-complete under certain one-side and two-side labeling schemes. Subsequently, approximation algorithms or heuristics are derived for the above intractable problems. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-70349858435&doi=10.7155%2fjgaa.00169&partnerID=40&md5=a1359eae8d21e684571a65da5b24be7e | DOI: | 10.7155/jgaa.00169 |
Appears in Collections: | 電機工程學系 |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.