Accelerate Incremental TSP Algorithms on Time Evolving Graphs with Partitioning Methods

Shalini Sharma,Jerry Chou

doi:10.3390/a15020064

Abstract

In time-evolving graphs, the graph changes at each time interval, and the previously computed results become invalid. We addressed this issue for the traveling salesman problem (TSP) in our previous work and proposed an incremental algorithm where the TSP tour is computed from the previous result instead of the whole graph. In our current work, we have mapped the TSP problem to three partitioning methods named vertex size attribute, edge attribute, and k-means; then, we compared the TSP tour results. We have also examined the effect of increasing the number of partitions on the total computation time. Through our experiments, we have observed that the vertex size attribute performs the best because of a balanced number of vertices in each partition.

Highlights

A graph is a commonly used data structure used to represent data with relationships.In the real world, graphs are used in the transportation systems, biological networks, social media graphs, and so on
We have addressed the challenge of Time-evolving graphs (TEG) by proposing an incremental algorithm [14]
We observed that the computation time can be significantly reduced for incremental algorithms (I-traveling salesman problem (TSP) and Ig-TSP) by using partitioning TSP algorithms (P-TSP and Pg-TSP), and the time reduction can be greater under a higher number of partitions

Summary

Introduction

A graph is a commonly used data structure used to represent data with relationships.In the real world, graphs are used in the transportation systems, biological networks, social media graphs, and so on. There can be the following update events on a graph: edge/vertex addition, deletion, and changes in weight. These update events change the structure of the TEG. These graphs are computed by building a set of graph snapshots of the data and applying the static graph techniques to them. The maintenance of graph snapshots is expensive when the volume and the velocity of update event increase and leads to wastage in terms of memory storage and computation power. This paper focuses on various domains, and the related work is divided into four sub-sections: namely, time-evolving graphs, the traveling salesman problem, incremental algorithm, and graph partitioning.

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