Programming and Testing a Two-Tree Algorithm

Vassilev, Tzvetalin; Ammerlaan, Joanna

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Approximation algorithms for metric tree cover and generalized tour and tree covers

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Given a weighted undirected graph , a tree (respectively tour) cover of an edge-weighted graph is a set of edges which forms a tree (resp. closed walk) and covers every other edge in the graph. The tree (resp. tour) cover problem is of finding a minimum weight tree (resp. tour) cover of . Arkin, Halldórsson and Hassin (1993) give approximation algorithms with factors respectively 3.5 and 5.5. Later Könemann, Konjevod, Parekh, and Sinha (2003) study the linear programming relaxations...

The triangles method to build $X$ -trees from incomplete distance matrices

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A method to infer $X$ -trees (valued trees having $X$ as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2 $n$ -3 distance values between the $n$ elements of $X$ , if they fulfill some explicit conditions. This construction is based on the mapping between $X$ -tree and a weighted generalized 2-tree spanning $X$ .