# Complexity and Approximation Results for the Min-Sum and Min-Max Disjoint Paths Problems

## Keywords:

Disjoint paths, min-sum, min-max, computational complexity, approximation algorithms## Abstract

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### Downloads

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## Published

2013-03-22

## How to Cite

*COMPUTING AND INFORMATICS*,

*32*(1), 23–45. Retrieved from https://www.cai.sk/ojs/index.php/cai/article/view/1465

## Issue

## Section

Articles