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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.
The simplest routing problem, called the Steiner tree problem, of finding the shortest route for one net in one layer with no obstacles and no design rules is known to be NP-complete, both in the case where all angles are allowed or if routing is restricted to only horizontal and vertical wires. [1]
The single-trunk Steiner tree is a tree that consists of a single horizontal segment and some vertical segments. A minimum single-trunk Steiner tree (MSTST) may be found in O ( n log n ) time. However simply finding all its edges requires linear time .
Examples of vertex covers Examples of minimum vertex covers. Formally, a vertex cover ′ of an undirected graph = (,) is a subset of such that ′ ′, that is to say it is a set of vertices ′ where every edge has at least one endpoint in the vertex cover ′.
Russia said Friday it had arrested suspected members of a Colombian cartel trying to smuggle tens of millions of dollars worth of cocaine into Europe.. The suspects were caught loading 570 ...
Office vacancies climbed more than 5% in six of the top 25 US markets this year, according to CommercialEdge. Sale prices, meanwhile, dropped again, down 9% from the average price in 2023.
Lower left: a Steiner tree of the vertices, length +. Lower right: the conjectured optimal solution, length 2 + 1 2 6 ≈ 2.639 {\displaystyle {\sqrt {2}}+{\tfrac {1}{2}}{\sqrt {6}}\approx 2.639} . In discrete geometry , an opaque set is a system of curves or other set in the plane that blocks all lines of sight across a polygon , circle, or ...
The AUKUS nuclear-powered submarine partnership with Australia will benefit the United States and is the kind of "burden sharing" deal that President-elect Donald Trump has talked about, U.S ...
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