Editing Open Problems:32
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: | ||
| β | {{ | + | {{DISPLAYTITLE:Problem 32: The Value of a Reverse Pass}} |
| β | | | + | {{Infobox |
| β | | | + | |label1 = Proposed by |
| + | |data1 = Andrew McGregor | ||
| + | |label2 = Source | ||
| + | |data2 = [[Workshops:Kanpur_2009|Kanpur 2009]] | ||
| + | |label3 = Short link | ||
| + | |data3 = http://sublinear.info/32 | ||
}} | }} | ||
Multi-pass stream algorithms have been designed for a range of problems including longest increasing subsequences {{cite|LibenNowellVZ-06|GuhaM-08}}, graph matchings {{cite|McGregor-05}}, and various geometric problems {{cite|ChanC-07}}. However, the existing literature almost exclusively considers the case when the multiple passes are in the same direction. One exception is recent work by Magniez et al. {{cite|MagniezMN-10}} on the '''DYCK'''${}_2$ problem: given a length $n$ string in the alphabet | Multi-pass stream algorithms have been designed for a range of problems including longest increasing subsequences {{cite|LibenNowellVZ-06|GuhaM-08}}, graph matchings {{cite|McGregor-05}}, and various geometric problems {{cite|ChanC-07}}. However, the existing literature almost exclusively considers the case when the multiple passes are in the same direction. One exception is recent work by Magniez et al. {{cite|MagniezMN-10}} on the '''DYCK'''${}_2$ problem: given a length $n$ string in the alphabet | ||
“${\tt (}$,${\tt )}$,${\tt [}$,${\tt ]}$”, determine whether it is well-parenthesized, i.e., it can be generated by the grammar $S\rightarrow {\tt (}S{\tt)} ~|~ {\tt [}S{\tt]} ~|~ SS ~|~ \epsilon$? For this problem it can be shown that with one forward and one reverse pass over the input, the problem can be solved with $O(\log^2 n)$ space. On the other hand, any algorithm using $O(1)$ forward passes and no reverse passes, requires $\Omega(\sqrt{n})$ space {{cite|ChakrabartiCKM-10|JainN-10}}. For what other natural problems is there such a large separation? | “${\tt (}$,${\tt )}$,${\tt [}$,${\tt ]}$”, determine whether it is well-parenthesized, i.e., it can be generated by the grammar $S\rightarrow {\tt (}S{\tt)} ~|~ {\tt [}S{\tt]} ~|~ SS ~|~ \epsilon$? For this problem it can be shown that with one forward and one reverse pass over the input, the problem can be solved with $O(\log^2 n)$ space. On the other hand, any algorithm using $O(1)$ forward passes and no reverse passes, requires $\Omega(\sqrt{n})$ space {{cite|ChakrabartiCKM-10|JainN-10}}. For what other natural problems is there such a large separation? | ||
