A self-stabilizing distributed file system is presented. The system constructs and maintains a spanning tree for each file volume. The spanning tree consists of the servers that have volume replicas and caches for the specific file volume. The spanning trees are constructed and maintained by selfstabilizing distributed algorithms. File system updates use the tree to implement file read and writ...

A linear-time algorithm for the minimum-ratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators.

This paper considers the conjecture by Grünbaum that every planar 3-connected graph has a spanning tree T such that both T and its co-tree have maximum degree at most 3. Here, the co-tree of T is the spanning tree of the dual obtained by taking the duals of the non-tree edges. While Grünbaum’s conjecture remains open, we show that every planar 3-connected graph has a spanning tree T such that b...

This paper considers k-minimum spanning tree problems. An existing solution algorithm based on tabu search, which was proposed by Katagiri et al., includes an iterative solving procedure of minimum spanning tree (MST) problems for subgraphs to obtain a local optimal solution of k-minimum spanning tree problems. This article provides a new tabu-searchbased approximate solution method that does n...

A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is an ultrametric. We show that every ultrametric minimum cost spanning tree game is reduced to a cost allocation game on a rooted tree. It follows that there exist O(n) time algorithms for computing the Shapley value, the nucleolus and the egalitarian allocation of the ultrametri...

Real-world images often admit many different segmentations that have nearly the same quality according to the underlying energy function. The diversity of these solutions may be a powerful uncertainty indicator. We provide the crucial prerequisite in the context of seeded segmentation with minimum spanning trees (i.e. edge-weighted watersheds). Specifically, we show how to efficiently enumerate...

A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is ultrametric. We show that every ultrametric minimum cost spanning tree game is a cost allocation game on a rooted tree. It follows that there exist optimal algorithms for computing the Shapley value, the nucleolus and the egalitarian allocation of the ultrametric minimum cost s...

Given n red and n blue points in the plane and a planar straight line matching between the red and the blue points, the matching can be extended into a bipartite planar straight line spanning tree. That is, any red-blue planar matching can be completed into a crossing-free red-blue spanning tree. Such a tree can be constructed in O(n log n) time. keywords: geometric graph, spanning tree, color