Rectilinear Spanning Trees Versus Bounding Boxes
نویسنده
چکیده
For a set P ⊆ R2 with 2 ≤ n = |P | < ∞ we prove that mst(P ) bb(P ) ≤ 1 √2 √ n + 32 where mst(P ) is the minimum total length of a rectilinear spanning tree for P and bb(P ) is half the perimeter of the bounding box of P . Since the constant 1 √ 2 in the above bound is best-possible, this result settles a problem that was mentioned by Brenner and Vygen (Networks 38 (2001), 126-139).
منابع مشابه
Notes on Binary Dumbbell Trees
Dumbbell trees were introduced in [1]. A detailed description of non-binary dumbbell trees appears in Chapter 11 of [3]. These notes show how binary dumbbell trees can be obtained, and how they can be used to construct, in O(n log n) time, a spanner of bounded degree and weight proportional to O(log n) times the weight of a minimum spanning tree. The reader is assumed to be familiar with the sp...
متن کاملOn Rectilinear Partitions with Minimum Stabbing Number
Let S be a set of n points in R, and let r be a parameter with 1 6 r 6 n. A rectilinear r-partition for S is a collection Ψ(S) := {(S1, b1), . . . , (St, bt)}, such that the sets Si form a partition of S, each bi is the bounding box of Si, and n/2r 6 |Si| 6 2n/r for all 1 6 i 6 t. The (rectilinear) stabbing number of Ψ(S) is the maximum number of bounding boxes in Ψ(S) that are intersected by a...
متن کاملWorst-case ratios of networks in the rectilinear plane
For point sets in the rectilinear plane we consider the following five measures of the interconnect length and prove bounds on the worst-case ratio: minimum Steiner tree, minimum star, clique, minimum spanning tree, and bounding box. In particular, we prove that for any set of n points: (n − 1) times the shortest Steiner tree is less or equal to the clique unless n = 4; and the minimum spanning...
متن کاملISPD: FOARS: FLUTE Based Obstacle-Avoiding Rectilinear Steiner Tree Construction
In this paper, we present an algorithm called FOARS for obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction. FOARS applies a top-down approach which first partitions the set of pins into several subsets uncluttered by obstacles. Then an obstacle-avoiding Steiner tree is generated for each subset by an obstacle aware version of the rectilinear Steiner minimal tree (RSMT) alg...
متن کاملRotated-Box Trees: A Lightweight c-Oriented Bounding-Volume Hierarchy
We introduce a new type of bounding-volume hierarchy, the c-oriented rotated-box tree, or c-rb-tree for short. A c-rb-tree uses boxes as bounding volumes, whose orientations come from a fixed set of predefined box orientations. We theoretically and experimentally compare our new c-rb-tree to two existing bounding-volumes hierarchies, namely c-dop-trees and box-trees.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 11 شماره
صفحات -
تاریخ انتشار 2004