0000000000449281
AUTHOR
Aleksejs Zajakins
Zemkvadrātisks algoritms koku ceļu apakšvirkņu uzdevumam
Darbā tiek apskatīts garākās kopīgās apakšvirknes uzdevuma vispārinājums uz kokiem. Tiek apskatīti divi vienāda izmēra koki, kuru virsotnes ir marķētas ar vienas kopas elementiem. Garākā kopīgā apakšvirkne tiek meklēta pāri visiem ieejas koku ceļu pāriem. Galvenais rezultāts ir algoritms, kas risina apskatīto uzdevumu laikā $O(n \log^3 n)$, kur $n$ ir abu ieejas koku virsotņu skaits.
All Classical Adversary Methods Are Equivalent for Total Functions
We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions and are equal to the fractional block sensitivity fbs( f ). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. This equivalence also implies that for total functions, the relational adversary is equivalent to a simpler lower bound, which we call rank-1 relational adversary. For partial functions, we show unbounded separations between fbs( f ) and other adversary bounds, as well as between the adversary bounds themselves. We also show that, for partial functions, fractional block sensitivity canno…