par Banerjee, Niranka;Varunkumar Jayapaul, Vo 
;Satti, Srinivasa Rao
Référence Lecture notes in computer science, 10976 LNCS, page (650-661)
Publication Publié, 2018
;Satti, Srinivasa RaoRéférence Lecture notes in computer science, 10976 LNCS, page (650-661)
Publication Publié, 2018
Article révisé par les pairs
| Résumé : | We are given a directed graph G(V, E) on n vertices and m edges where each edge has a positive weight associated with it. The influx of a vertex is defined as the difference between the sum of the weights of edges entering the vertex and the sum of the weights of edges leaving the vertex. The goal is to find a graph (Formula Presented) such that the influx of each vertex in (Formula Presented) is same as the influx of each vertex in G(V, E) and (Formula Presented) is minimal. We show that 1.finding the optimal solution for this problem is NP-hard,2.the optimal solution has at most (Formula Presented) edges, and we give an algorithm to find one such solution with at most (Formula Presented) edges in (Formula Presented) time, and3.for one variant of the problem where we can delete as well as add extra edges to the graph, we can compute a solution that is within a factor 3 / 2 from the optimal solution. |
