TY - JOUR
AU - Zhang, Peng
AU - Zhao, Wenbo
AU - Zhu, Daming
PY - 2013/03/22
Y2 - 2023/03/29
TI - Complexity and Approximation Results for the Min-Sum and Min-Max Disjoint Paths Problems
JF - COMPUTING AND INFORMATICS
JA - Comput. Inform.
VL - 32
IS - 1
SE - Articles
DO -
UR - https://www.cai.sk/ojs/index.php/cai/article/view/1465
SP - 23-45
AB - Given a graph G=(V, E) and k source-sink pairs (s1, t1), …, (sk, tk) with each si, ti V, the Min-Sum Disjoint Paths problem asks to find k disjoint paths connecting all the source-sink pairs with minimized total length, while the Min-Max Disjoint Paths problem asks for k disjoint paths connecting all the source-sink pairs with minimized length of the longest path. We show that the weighted Min-Sum Disjoint Paths problem is FPNP-complete in general graphs, and the unweighted Min-Sum Disjoint Paths problem and the unweighted Min-Max Disjoint Paths problem cannot be approximated within m(m1-1) for any constant > 0 even in planar graphs, assuming P P NP, where m is the number of edges in G. We give for the first time a simple bicriteria approximation algorithm for the unweighted Min-Max Edge-Disjoint Paths problem and the weighted Min-Sum Edge-Disjoint Paths problem, wi
ER -