We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 14 November 2024
An, Kleinberg, and Shmoys were the first to beat Christofides’ algorithm for Path TSP. Their algorithm, which they called Best-of-Many Christofides, is very natural: Since an LP solution can be written as convex combination of spanning trees, we can do parity correction on each of these trees and output the best of the resulting tours. It turns out that this yields a better guarantee than the 5/3 that Christofides’ algorithm yields.
In this chapter, we analyze this algorithm and study various follow-up works that have yielded better and better approximation ratios; some of them also apply to general T-tours. This includes a structured decomposition into spanning trees (by Gottschalk and Vygen), Best-of-Many Christofides with lonely edge deletion (by Sebő and van Zuylen), and Traub’s T-tour algorithm.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
