A Subgradient Method to Improve Approximation Ratio in the Minimum Latency Problem

Abstract

The Minimum Latency Problem (MLP) is a combinatorial optimization problem which has many practical applications. Recently, several approximation algorithms with guaranteed approximation ratio have been proposed to solve the MLP problem. These algorithms start with a set of solutions of the k −MST or k −troll problem, then convert the solutions into Eulerian tours, and finally, concatenate these Eulerian tours to obtain a MLP tour. In this paper, we propose an algorithm based on the principles of the subgradient method. It still uses the set of solutions of the k −MST or k −troll problem as an input, then modifies each solution into a tour with cost smaller than that of Eulerian tour and finally, uses obtained tours to construct a MLP tour. Since the low cost tours are used to build a MLP tour, we can expect the approximation ratio of obtained algorithm will be improved. In order to illustrate this intuition, we have evaluated the algorithm on five benchmark datasets. The experimental results show that approximation ratio of our algorithm is improved compared to the best well-known approximation algorithms.