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: 28 January 2010
One of the simplest combinatorial-optimization problems is that of finding a minimum-weight dipath in an edge-weighted digraph (under some natural restrictions on the weight function). Not only are there rather simple algorithms for this problem, but algorithms for the minimum-weight dipath problem are fundamental building blocks for developing solution methods for more complicated problems.
Let G be a strict digraph. A v w diwalk is a sequence of edges ei, 1 ≤ i ≤ p (with p ≥ 0), such that t(e1) = v (if p > 0), h(ep) = w (if p > 0), and h(ei) = t(ei+1), for 1 ≤ i < p. Neither the edges nor the vertices need be distinct. The v w diwalk imputes the sequence of vertices v = t(e1),h(e1) = t(e2), h(e2) = t(e3), …, h(ep-1) = t(ep), h(ep) = w. If no vertex in this imputed vertex sequence is repeated, then the vw diwalk is called a vw dipath. In such a case, every vertex of the imputed sequence other than v and w is called an interior vertex. Note that the empty sequence of edges is a vv diwalk for any vertex v; the associated imputed sequence of vertices is also empty, so the empty sequence of edges is a vv dipath. If v = w, and the only repetition in the imputed vertex sequence is the consonance of the first element with the last, then the diwalk is a dicycle.
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.
