BALANCED PARTITION OF MINIMUM SPANNING TREES

Balanced Partition of Minimum Spanning Trees

To better handle situations where additional resources are available to carry out a task, many problems from the manufacturing industry involve “optimally” dividing a task into k smaller tasks. We consider the problem of partitioning a given set S of n points (in the plane) into k subsets, S1, . . . ,Sk, such that max16i6k |MST (Si)| is minimized. A variant of this problem arises in the shipbui...

Geometric Minimum Spanning Trees

Let S be a set of n points in < d. We present an algorithm that uses the well-separated pair decomposition and computes the minimum spanning tree of S under any Lp or polyhedral metric. It has an expected running time of O(n logn) for uniform distributions. Experimentalresults show that this approachis practical. Under a variety of input distributions, the resultingimplementation is robust and ...

Minimum Spanning Trees∗

1 Background Members of some secret party want to shutdown some high risk communication channals, while preserving low risk channals to ensure that members are still connected in the secret network.

Minimum Spanning Trees

Let G =< V,E > be a connected graph with real-valued edge weights: w : E → R, having n vertices and m edges. A spanning tree in G is an acyclic subgraph of G that includes every vertex of G and is connected; every spanning tree has exactly n− 1 edges. A minimum spanning tree (MST) is a spanning tree of minimum weight which is defined to be the sum of the weights of all its edges. Our problem is...

Geometri Minimum Spanning Trees