---
title: "The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound"
authors:
  - "Jingyang Zhao"
  - "Mingyu Xiao"
doi: "10.24963/ijcai.2021/578"
url: "https://ijcai.org/proceedings/2021/578"
pdf: "https://ijcai.org/proceedings/2021/0578.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "4206-4212"
track: "Main Track"
keywords:
  - "Planning and Scheduling: Planning Algorithms"
  - "Planning and Scheduling: Theoretical Foundations of Planning"
  - "Planning and Scheduling: Scheduling"
---

# The Traveling Tournament Problem with Maximum Tour Length Two: A Practical Algorithm with An Improved Approximation Bound

Jingyang Zhao, Mingyu Xiao

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 4206-4212. DOI: [10.24963/ijcai.2021/578](https://doi.org/10.24963/ijcai.2021/578)

## Abstract

The Traveling Tournament Problem is a well-known benchmark problem in tournament timetabling, which asks us to design a schedule of home/away games of n teams (n is even) under some feasibility requirements such that the total traveling distance of all the n teams is minimized. In this paper, we study TTP-2, the traveling tournament problem where at most two consecutive home games or away games are allowed, and give an effective algorithm for n/2 being odd. Experiments on the well-known benchmark sets show that we can beat previously known solutions for all instances with n/2 being odd by an average improvement of 2.66%. Furthermore, we improve the theoretical approximation ratio from 3/2+O(1/n) to 1+O(1/n) for n/2 being odd, answering a challenging open problem in this area.