On a random directed spanning tree
نویسندگان
چکیده
منابع مشابه
On A Random Directed Spanning Tree
We study the asymptotic properties of a minimal spanning tree formed by n points uniformly distributed in the unit square, where the minimality is amongst all rooted spanning trees with a direction of growth. We show that the number of branches from the root of this tree, the total length of these branches, and the length of the longest branch each converge weakly. This model is related to the ...
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For n i.i.d. uniform points in [0, 1]d, d ≥ 2, let Ln be the total distance from the origin to all the minimal points under the coordinate-wise partial order (this is also the total length of rooted edges of a minimal directed spanning tree on the given n random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of Ln, and show that Ln satisfies a central limit theore...
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In Bhatt and Roy’s minimal directed spanning tree (MDST) construction for a random partially ordered set of points in the unit square, all edges must respect the “coordinatewise” partial order and there must be a directed path from each vertex to a minimal element. We study the asymptotic behaviour of the total length of this graph with power weighted edges. The limiting distribution is given b...
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Consider a directed graph G = (V,E) with n vertices and a root vertex r ∈ V . The DMDST problem for G is one of constructing a spanning tree rooted at r, whose maximal degree is the smallest among all such spanning trees. The problem is known to be NP-hard. A quasipolynomial time approximation algorithm for this problem is presented. The algorithm finds a spanning tree whose maximal degree is a...
متن کاملOn the Length of a Random Minimum Spanning Tree
We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞ E(Ln) = ζ(3) and show that E(Ln) = ζ(3) + c1 n + c2+o(1) n4/3 where c1, c2 are explicitly defined constants.
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2004
ISSN: 0001-8678,1475-6064
DOI: 10.1017/s0001867800012854