Let Q(n) be the n-dimensional hypercube, and X a set of points in Q(n). The Steiner problem for the hypercube is to find the smallest number L(n,X) of edges in any subtree of Q(n) which spans X. Let W(k,n) be the set of points in Q(n) having weight k, where we normalize k+1 ≤ n 2 . We apply a result of Frankl and Rödl on the generalized Turan problem for hypergraphs to

A Fixed-Parameter Tractable (FPT) ρ-approximation algorithm for a minimization (resp. maximization) parameterized problem P is an FPT-algorithm that, given an instance (x, k) ∈ P computes a solution of cost at most k · ρ(k) (resp. k/ρ(k)) if a solution of cost at most (resp. at least) k exists; otherwise the output can be arbitrary. For well-known intractable problems such as the W[1]-hard Cliq...

Two vertex-labelled polygons are compatible if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations—for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible n-vertex polygonal regions can be extended to compatible triangulations b...

In this note we prove two results on the quantitative illumination parameter f (d) of the unit ball of a d-dimensional normed space introduced by K. Bezdek (1992). The first is that f (d) = O(2dd2 log d). The second involves Steiner minimal trees. Let v(d) be the maximum degree of a vertex, and s(d) of a Steiner point, in a Steiner minimal tree in a d-dimensional normed space, where both maxima...

Let T be a distinguished subset of vertices in a graph G. A T Steiner tree is a subgraph of G that is a tree and that spans T . Kriesell conjectured that G contains k pairwise edge-disjoint T -Steiner trees provided that every edge-cut of G that separates T has size ≥ 2k. When T = V (G) a T -Steiner tree is a spanning tree and the conjecture is a consequence of a classic theorem due to Nash-Wil...

We show that the survivable bottleneck Steiner tree problem in normed planes can be solved in polynomial time when the number of Steiner points is constant. This is a fundamental problem in wireless ad-hoc network design where the objective is to design networks with efficient routing topologies. Our result holds for a general definition of survivability and for any norm whose ball is specified...

In this paper we develop streaming algorithms for the diameter problem and the k-center clustering problem in the sliding window model. In this model we are interested in maintaining a solution for the N most recent points of the stream. In the diameter problem we would like to maintain two points whose distance approximates the diameter of the point set in the window. Our algorithm computes a ...

A graph is k-domination-critical if γ(G)=k, and for any edge e not in G, γ(G+e) = k-1. In this paper we show that the diameter of a domination k-critical graph with k≥2 is at most 2k-2. We also show that for every k≥2, there is a k-domination-critical graph having diameter 3 2 k 1 −     . We also show that the diameter of a 4-domination-critical graph is at most 5.

Using the CHARA Array and the Palomar Testbed Interferometer, the chemically peculiar star k Boötis has been spatially resolved.We havemeasured the limb darkened angular diameter to be LD 1⁄4 0:533 0:029mas, corresponding to a linear radius of R? 1⁄4 1:70 0:10R . Themeasured angular diameter yields an effective temperature for kBoo of TeA 1⁄4 8887 242 K. Based on literature surface gravity esti...

We present a new deterministic algorithm for the Steiner tree problem in weighted graphs. Its running time is O(nk2k+log2 k log2 n), where n is the number of vertices and k is the number of terminals. This is faster than all previously known algorithms if 2 log n(log log n)3 < k < (n − log n)/2. Our algorithm is based on a new tree composition theorem.