Abstract (EN)

This paper investigates two problems related to the determination of critical edges for the minimum cost assignment problem. Given a complete bipartite balanced graph with nn vertices on each part and with costs on its edges, kkMost Vital Edges Assignment consists of determining a set of kk edges whose removal results in the largest increase in the cost of a minimum cost assignment. A dual problem, Min Edge Blocker Assignment, consists of removing a subset of edges of minimum cardinality such that the cost of a minimum cost assignment in the remaining graph is larger than or equal to a specified threshold. We show that kkMost Vital Edges Assignment is NPNP-hard to approximate within a factor c<2c<2 and Min Edge Blocker Assignment is NPNP-hard to approximate within a factor 1.361.36. We also provide an exact algorithm for kkMost Vital Edges Assignment that runs in O(nk+2)O(nk+2). This algorithm can also be used to solve exactly Min Edge Blocker Assignment.