Finding the most vital node of a shortest path
نویسندگان
چکیده
منابع مشابه
Finding the Most Vital Node of a Shortest Path
In an undirected, 2-node connected graph G = (V,E) with positive real edge lengths, the distance between any two nodes r and s is the length of a shortest path between r and s in G. The removal of a node and its incident edges from G may increase the distance from r to s. A most vital node of a given shortest path from r to s is a node (other than r and s) whose removal from G results in the la...
متن کاملA faster computation of the most vital edge of a shortest path
Let PG(r, s) denote a shortest path between two nodes r and s in an undirected graph G = (V ,E) such that |V | = n and |E| = m and with a positive real length w(e) associated with any e ∈ E. In this paper we focus on the problem of finding an edge e∗ ∈ PG(r, s) whose removal is such that the length of PG−e∗(r, s) is maximum, where G − e∗ = (V ,E \ {e∗}). Such an edge is known as the most vital ...
متن کاملA Refined Complexity Analysis of Finding the Most Vital Edges for Undirected Shortest Paths
We study the NP-hard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices s and t, the goal is to delete as few edges as possible in order to increase the length of the (new) shortest st-path as much as possible. This scenario has been mostly studied from the viewpoin...
متن کاملFinding the Anti-block Vital Edge of a Shortest Path Between Two Nodes
Let PG(s, t) denote a shortest path between two nodes s and t in an undirected graph G with nonnegative edge weights. A detour at a node u ∈ PG(s, t) = (s, . . . , u, v, . . . , t) is defined as a shortest path PG−e(u, t) from u to t which does not make use of (u, v). In this paper, we focus on the problem of finding an edge e = (u, v) ∈ PG(s, t) whose removal produces a detour at node u such t...
متن کاملThe Complexity of Finding Most Vital
Let G(V; E) be a graph (either directed or undirected) with a non-negative length`(e) associated with each arc e in E. For two speciied nodes s and t in V , the k most vital arcs (or nodes) are those k arcs (nodes) whose removal maximizes the increase in the length of the shortest path from s to t. We prove that nding the k most vital arcs (or nodes) is NP-hard, even when all arcs have unit len...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2003
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(02)00438-3