Straight-line Drawings of Binary Trees with Linear Area and Arbitrary Aspect Ratio
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چکیده
Trees are usually drawn planar, i.e. without any edge-crossings. In this paper, we investigate the area requirement of (non-upward) planar straight-line grid drawings of binary trees. Let T be a binary tree with n nodes. We show that T admits a planar straight-line grid drawing with area O(n) and with any pre-specified aspect ratio in the range [n− , n ], where is any constant, such that 0 < < 1. We also show that such a drawing can be constructed in O(n logn) time. In particular, our result shows that optimal area (equal to O(n)) and optimal aspect ratio (equal to 1) are simultaneously achievable for such drawings. Article Type Communicated by Submitted Revised Regular Paper Xin He April 2003 May 2004 Research supported by NSF CAREER Award IIS-9985136, NSF CISE Research Infrastructure Award No. 0101244, and Mark Diamond Research Grant No. 13-Summer2003 from GSA of The State University of New York. This research was performed while the second author was at the Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY. A preliminary version of the paper was presented at the Tenth International Symposium on Graph Drawing, Irvine, CA, September,
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تاریخ انتشار 2002