Earlier quoted context omitted.
This book is published in 2013. Earlier than this arxiv paper.
Do you suggest that they've used your findings without referencing you? You can make an inquiry I believe. Other than that, if their method is completely different or they've arrived to the same solution independently - there is nothing wrong. It is not about the competition who was first, isn't it?
In maths it is thought to be beneficial to come up with a diferent proof of the same theorem though, so maybe in computing the similar idea that coming up with another implementation/demonstration/proof has value too