On the space complexity of one-pass compression
| dc.creator | Gagie, Travis | |
| dc.date | 2006-11-21 | |
| dc.date.accessioned | 2026-07-07T08:18:04Z | |
| dc.date.available | 2026-07-07T08:18:04Z | |
| dc.description | We study how much memory one-pass compression algorithms need to compete with the best multi-pass algorithms. We call a one-pass algorithm an (f (n, \ell))-footprint compressor if, given $n$, $\ell$ and an $n$-ary string $S$, it stores $S$ in ((\rule{0ex}{2ex} O (H_\ell (S)) + o (\log n)) |S| + O (n^{\ell + 1} \log n)) bits -- where (H_\ell (S)) is the $\ell$th-order empirical entropy of $S$ -- while using at most (f (n, \ell)) bits of memory. We prove that, for any (ε> 0) and some (f (n, \ell) \in O (n^{\ell + ε} \log n)), there is an (f (n, \ell))-footprint compressor; on the other hand, there is no (f (n, \ell))-footprint compressor for (f (n, \ell) \in o (n^\ell \log n)). | |
| dc.identifier | https://arxiv.org/abs/cs/0611099 | |
| dc.identifier | http://arxiv.org/abs/cs/0611099 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134307 | |
| dc.subject | Information Theory | |
| dc.subject | H.1.1 | |
| dc.title | On the space complexity of one-pass compression | |
| dc.type | text |