@article{Zhang_Zhao_Zhu_2013, title={Complexity and Approximation Results for the Min-Sum and Min-Max Disjoint Paths Problems}, volume={32}, url={https://www.cai.sk/ojs/index.php/cai/article/view/1465}, abstractNote={Given a graph G=(V, E) and k source-sink pairs (s1, t1), &hellip;, (sk, tk) with each si, ti&nbsp; 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&nbsp;&nbsp; &gt; 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}, number={1}, journal={COMPUTING AND INFORMATICS}, author={Zhang, Peng and Zhao, Wenbo and Zhu, Daming}, year={2013}, month={Mar.}, pages={23–45} }