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WALCOM 2017: WALCOM: Algorithms and Computation pp 448-459

# The Time Complexity of the Token Swapping Problem and Its Parallel Variants

• Jun Kawahara
• Toshiki Saitoh
• Ryo Yoshinaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10167)

## Abstract

The token swapping problem (TSP) and its colored version are reconfiguration problems on graphs. This paper is concerned with the complexity of the TSP and two new variants; namely parallel TSP and parallel colored TSP. For a given graph where each vertex has a unique token on it, the TSP requires to find a shortest way to modify a token placement into another by swapping tokens on adjacent vertices. In the colored version, vertices and tokens are colored and the goal is to relocate tokens so that each vertex has a token of the same color. Their parallel versions allow simultaneous swaps on non-incident edges in one step. We investigate the time complexity of several restricted cases of those problems and show when those problems become tractable and remain intractable.

## Keywords

Approximation Algorithm Polynomial Time Bipartite Graph Complete Graph Initial Configuration
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer International Publishing AG 2017

## Authors and Affiliations

1. 1.Graduate School of Information ScienceNAISTIkomaJapan
2. 2.Graduate School of EngineeringKobe UniversityKobeJapan
3. 3.Graduate School of Information SciencesTohoku UniversitySendaiJapan