Stability and Robustness: Reliability in the World of Uncertainty

Greedy Construction HeuristicThe Central TreeProblemHeuristics for theCTPFinal RemarksAlgorithm Greedy Construction Heuristic(G = (E, V ))Input: A connected graph G = (E, V )Output: The edges E 0 of a potential central tree T 01. Initialize G ′ = G, E 0 = {}, LC = [G]2. while |E 0 | < |V | − 13. do Take an arbitrary element C from LC4. Apply MINCUT(C) and return the set of edgesMINCUTSET(C)5. for all edges e ∈ MINCUTSET(C)6. do if E 0 + {e} does not contain cycles7. then E 0 = E 0 + {e}8. else do nothing9. Update LC by removing C and adding thosecomponents of C ′ = C − MINCUTSET(C) whichare not an isolated vertex10. return E 0Heuristics for the Central Tree Problem Yury Nikulin - p. 18/33