Multi-source Trees: Algorithms for Minimizing Eccentricity Cost Metrics

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 functionÈd∈D maxs∈S dT (s, d) (the SSET cost function Ès∈S maxd∈D dT (s, 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...

• Type: Conference
• Year: 2005
• Where: ISAAC
• Authors: Paraskevi Fragopoulou, Stavros D. Nikolopoulos, Leonidas Palios
• Keywords: Eccentricity Problem, ISAAC 2005, Source Eccentricity Problem, Vertex Eccentricity Problem