Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
A polynomial time approximation scheme for minimum routing cost spanning trees
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Multi-source spanning trees: algorithms for minimizing source eccentricities
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
The complexity of minimizing certain cost metrics for k-source spanning trees
Discrete Applied Mathematics
Multicast routing with end-to-end delay and delay variation constraints
IEEE Journal on Selected Areas in Communications
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We consider generalizations of the k-source sum of vertex eccentricity problem (k-SVET) and the k-source sum of source eccentricity problem (k-SSET) [1], which we call SDET and SSET, respectively, and provide efficient algorithms for their solution. The SDET (SSET, resp.) problem is defined as follows: given a weighted graph G and sets S of source nodes and D of destination nodes, which are subsets of the vertex set of G, construct a tree-subgraph T of G which connects all sources and destinations and minimizes the SDET cost function $\sum_{d\in {\it D}}{\it max}_{s \in {\it S}}{\it d}_{T}({\it s},{\it d})$ (the SSET cost function $\sum_{s\in {\it S}}{\rm max}_{d \in {\it D}}{\it d}_{T}({\it s},{\it d})$, respectively). We describe an O(nm log n)-time algorithm for the SDET problem and thus, by symmetry, to the SSET problem, where n and m are the numbers of vertices and edges in G. The algorithm introduces efficient ways to identify candidates for the sought tree and to narrow down their number to O(m). Our algorithm readily implies O(nm log n)-time algorithms for the k-SVET and k-SSET problems as well.