Steiner trees have been extensively studied in the context of weighted graphs. The prototype is, arguably, the Steiner tree problem in graphs. Let G = (V, E) be an undirected graph with non-negative edge weights c and let S ⊆ V be a subset of vertices, called terminals. A Steiner tree is a tree in G that spans S. There are two versions of the problem: in the optimization problem associated with Steiner trees, the task is to find a minimum-weight Steiner tree; in the decision pr… WebFind maximum number of edge-disjoint Steiner trees inG. The two extreme cases of the problem are fundamental theorems: If T = 2 =⇒ Steiner trees are basically paths between two nodes =⇒ Theorem (Menger 1920’s): The number of edge-disjoint paths between two vertices u and v is equal to the minimum number of edges whose removal
Hardness - math.uwaterloo.ca
WebFeb 16, 2024 · Let G = (V,E) be an undirected graph with a distinguished set of terminal vertices K ⊆ V, K ≥ 2. A K‐Steiner tree T of G is a tree containing the terminal vertex‐set K, where any vertex of degree … Expand WebFor packing edge-disjoint Steiner trees of undirected graphs, we show APX-hardness for four terminals. For packing Steiner-node-disjoint Steiner trees of undirected graphs, we show a logarithmic hardness result, and give an approximation guarantee ofO (√n logn), … importance of time value money
Perfect Omniscience, Perfect Secrecy and Steiner Tree Packing
WebThis problem, now called the Steiner tree problem, was initially of importance only within the context of land surveying. Recent applications, as diverse as VLSI-layout and the study of phylogenetic trees, have, however, lead to significant interest in the problem. The resulting progress has uncovered fascinating connections to and among graph ... WebSteiner trees. Giv en an undirected graph G = (V ; E) and a set of terminal no des T V, a Steiner tr e is a connected, acyclic subgraph that con tains all the terminal no des (non terminal no des, whic h are called Steiner no des, optional). The basic problem of P ac king Edge-disjoin t Undirected Steiner trees (PEU for short) is to nd as man y ... WebNov 1, 2010 · Request PDF Packing Steiner trees on four terminals Let A be a set of vertices of some graph G. An A-tree is a subtree of G containing A, and A is called k-edge-connected in G if every set of ... importance of tissue culture