Min-Sum 2-Paths Problems

An orientation of an undirected graph G is a directed graph obtained by replacing each edge {u, v} of G by exactly one of the arcs (u, v) or (v, u). In the min-sum k-paths orientation problem, the input is an undirected graph G and ordered pairs (si, ti), where i ∈ {1, 2, . . . , k}. The goal is to find an orientation of G that minimizes the sum over every i ∈ {1, 2, . . . , k} of the distance from si to ti. In the min-sum k edge-disjoint paths problem the input is the same, however the goal is to find for every i ∈ {1, 2, . . . , k} a path between si and ti so that these paths are edge-disjoint and the sum of their lengths is minimum. Note that, for every fixed k ≥ 2, the question of NP-hardness for the min-sum k-paths orientation problem and the min-sum k edge-disjoint paths problem have been open for more than three decades. We study the complexity of these problems when k = 2. We exhibit a PTAS for the min-sum 2-paths orientation problem. A by-product of this PTAS is a ...

• Type: Journal
• Year: 2016
• Where: MST
• Authors: Trevor I. Fenner, Oded Lachish, Alexandru Popa
• Keywords: Hardware, MST 2016