Large-c conformal (n ? 6)-point blocks with superlight weights and holographic Steiner trees

Approximating Steiner trees in graphs with restricted weights

We analyze the approximation ratio of the average distance heuristic for the Steiner tree problem on graphs, and prove nearly tight bounds for the cases of complete graphs with binary weights f1; dg, or weights in the interval 1; d], where d 2. The improvement over other analyzed algorithms is a factor of about e 2:718.

Approximating Minimum Steiner Point Trees in Minkowski

Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at most 1 and the number of additional points is minimized. We propose using Steiner minimal trees to approximate minimum Steiner point trees. It is shown that in arbitrary metric spaces this gives a performance differe...

Towards a holographic dual of large - N c QCD

We study Nf D6-brane probes in the supergravity background dual to Nc D4branes compactified on a circle with supersymmetry-breaking boundary conditions. In the limit in which the resulting Kaluza–Klein modes decouple, the gauge theory reduces to nonsupersymmetric, four-dimensional QCD with Nc colours and Nf ≪ Nc flavours. As expected, this decoupling is not fully realised within the supergravit...

Steiner Trees and Steiner Forests

Approximating Steiner Networks with Node Weights

The (undirected) Steiner Network problem is as follows: given a graphG = (V, E) with edge/node-weights and edge-connectivity requirements {r(u, v) : u, v ∈ U ⊆ V }, find a minimumweight subgraph H of G containing U so that the uv-edge-connectivity in H is at least r(u, v) for all u, v ∈ U . The seminal paper of Jain [Combinatorica, 21 (2001), pp. 39–60], and numerous papers preceding it, consid...