A Sketch-First Approach for Finding TSP

Abstract

Travel planning is one of the most important issues in location-based services (LBS), and TSP (traveling salesman problem) is to find the shortest tour that traverses all the given points exactly once. Given the hardness of TSP as an NP-hard problem, a large number of heuristic methods are proposed to find a tour efficiently. Here, the heuristics proposed are based on a similar idea that is to expand a partial tour by adding points one by one in different ways until all points are visited. In this paper, we study TSP query with a given set of points \(Q\). We propose a new heuristic called Sketch-First, which is different from the existing approaches. By Sketch-First, we select a set of points out of \(Q\), forming a sketch of \(Q\), and add the points that are not in the sketch back to the sketch to obtain the answer for \(Q\). The sketch gives a global picture on the points, and can be used to guide to add the other points back effectively. We discuss the heuristics to find a sketch for \(Q\). Our approach is based on the observation that a better sketch with the same number of points is the sketch over which its optimal tour is larger in length. In addition, as the number of such points is to be small, we can find the optimal tour for the sketch. We discuss our methods, and conduct extensive experiments to show the effectiveness and efficiency of our methods.