# Independent Tree Spanners

Fault-Tolerant Spanning Trees with Constant Distance Guarantees (Extended Abstract)
• Dagmar Handke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

## Abstract

For any fixed parameter t ≥ 1, a tree t-spanner of a graph G is a spanning tree T of G such that the distance between every pair of vertices in T is at most t times their distance in G. In this paper, we incorporate a concept of fault-tolerance by examining independent tree t-spanners. Given a root vertex r, this is a pair of tree t-spanners, such that the two paths from any vertex to r are edge (resp., internally vertex) disjoint. It is shown that a pair of independent tree 2-spanners can be found in linear time, whereas the problem for arbitrary t ≥ 4 is $$\cal NP$$-complete.

As a less restrictive concept, we treat tree t-root-spanners, where the distance constraint is relaxed. Here, we show that the problem of finding an independent pair of such subgraphs is $$\cal NP$$-complete for all t. As a special case, we then consider direct tree t-root-spanners. These are tree t-root-spanners where paths from any vertex to the root have to be detour-free. In the edge independent case, a pair of these can be found in linear time for all t, whereas the vertex independent case remains $$\cal NP$$-complete.

## Keywords

Span Tree Parent Level Truth Assignment Span Subgraph Root Vertex
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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