Editing Open Problems:14
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 1: | Line 1: | ||
{{Header | {{Header | ||
| + | |title=Graph Distances | ||
|source=kanpur06 | |source=kanpur06 | ||
|who=Andrew McGregor | |who=Andrew McGregor | ||
| Line 8: | Line 9: | ||
Clearly, an $(\alpha,\beta)$-spanner gives an $\alpha+\beta/d_G(u,v)$ approximation to $d_G(u,v)$. | Clearly, an $(\alpha,\beta)$-spanner gives an $\alpha+\beta/d_G(u,v)$ approximation to $d_G(u,v)$. | ||
Since a spanner is constructed independently of $u$ and $v$ it is perhaps surprising that this approach gives nearly optimal results for approximating $d_G(u,v)$ in a single pass {{cite|FeigenbaumKMSZ-05}}. It is unclear whether there is a better approach for multiple pass algorithms. Clearly, $d_G(u,v)$ can be computed exactly in $d_G(u,v)$ passes but for $d_G(u,v)$ large this is infeasible. Can we do better? For example, how well can $d_G(u,v)$ be approximated in $O(\log n)$ passes? What if the edges arrived in random order? | Since a spanner is constructed independently of $u$ and $v$ it is perhaps surprising that this approach gives nearly optimal results for approximating $d_G(u,v)$ in a single pass {{cite|FeigenbaumKMSZ-05}}. It is unclear whether there is a better approach for multiple pass algorithms. Clearly, $d_G(u,v)$ can be computed exactly in $d_G(u,v)$ passes but for $d_G(u,v)$ large this is infeasible. Can we do better? For example, how well can $d_G(u,v)$ be approximated in $O(\log n)$ passes? What if the edges arrived in random order? | ||
| β | |||
| β | |||
| β | |||
