Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

A cycle cover of a graph is a spanning subgraph each node of which is part of exactly one simple cycle. A k-cycle cover is a cycle cover where each cycle has length at least k. Given a complete directed graph with edge weights zero and one, Max-k-DCC(0, 1) is the problem of finding a k-cycle cover with maximum weight. We present a 2 3 approximation algorithm for Max-k-DCC(0, 1) with running time O(n5/2). This algorithm yields a 4 3 approximation algorithm for Min-k-DCC(1, 2) as well. Instances of the latter problem are complete directed graphs with edge weights one and two. The goal is to find a k-cycle cover with minimum weight. We particularly obtain a 2 3 approximation algorithm for the asymmetric maximum traveling salesman problem with distances zero and one and a 4 3 approximation algorithm for the asymmetric minimum traveling salesman problem with distances one and two. As a lower bound, we prove that Max-k-DCC(0, 1) for k 3 and Maxk-UCC(0, 1) (finding maximum weight cycle cove...

• Type: Journal
• Year: 2005
• Where: ALGORITHMICA
• Authors: Markus Bläser, Bodo Manthey
• Keywords: Algorithm, ALGORITHMICA 2005, Complete Directed Graph, K-cycle Cover