The Steiner k-eccentricity of a vertex is the maximum Steiner distance over all k-sets each of which contains the given vertex,where the Steiner distance of a vertex set is the size of a minimum Steiner tree on this s...The Steiner k-eccentricity of a vertex is the maximum Steiner distance over all k-sets each of which contains the given vertex,where the Steiner distance of a vertex set is the size of a minimum Steiner tree on this set.Since the minimum Steiner tree problem is well-known NP-hard,the Steiner k-eccentricity is not so easy to compute.This paper attempts to efficiently solve this problem on block graphs and general graphs with limited cycles.A block graph is a graph in which each block is a clique,and is also called a clique-tree.On block graphs,we propose an O(k(n+m))-time algorithm to compute the Steiner k-eccentricity of a vertex where n and m are respectively the order and size of a block graph.On general graphs with limited cycles,we take the cyclomatic numberν(G)as a parameter which is the minimum number of edges of G whose removal makes G acyclic,and devise an O(n^(ν(G)+1)(n(G)+m(G)+k))-time algorithm.展开更多
基金Supported by Guizhou Provincial Basic Research Program (Natural Science)(No.ZK[2022]020)。
文摘The Steiner k-eccentricity of a vertex is the maximum Steiner distance over all k-sets each of which contains the given vertex,where the Steiner distance of a vertex set is the size of a minimum Steiner tree on this set.Since the minimum Steiner tree problem is well-known NP-hard,the Steiner k-eccentricity is not so easy to compute.This paper attempts to efficiently solve this problem on block graphs and general graphs with limited cycles.A block graph is a graph in which each block is a clique,and is also called a clique-tree.On block graphs,we propose an O(k(n+m))-time algorithm to compute the Steiner k-eccentricity of a vertex where n and m are respectively the order and size of a block graph.On general graphs with limited cycles,we take the cyclomatic numberν(G)as a parameter which is the minimum number of edges of G whose removal makes G acyclic,and devise an O(n^(ν(G)+1)(n(G)+m(G)+k))-time algorithm.
