Open AccessHardness Results for Dynamic Problems by Extensions of Fredman and Saks’ Chronogram Method
Author(s) -
Thore Husfeldt,
Theis Rauhe
Publication year - 1997
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v4i32.18958
Subject(s) - nondeterministic algorithm , string (physics) , reachability , upper and lower bounds , combinatorics , prefix , mathematics , discrete mathematics , computer science , omega , mathematical analysis , physics , quantum mechanics , mathematical physics , linguistics , philosophy
We introduce new models for dynamic computation based on the cell probe model of Fredman and Yao. We give these models access to nondeterministic queries or the right answer +-1 as an oracle. We prove that for the dynamic partial sum problem, these new powers do not help, the problem retains its lower bound of Omega(log n/log log n). From these results we easily derive a large number of lower bounds of order Omega(log n/log log n) for conventional dynamic models like the random access machine. We prove lower bounds for dynamic algorithms for reachability in directed graphs, planarity testing, planar point location, incremental parsing, fundamental data structure problems like maintaining the majority of the prefixes of a string of bits and range queries. We characterise the complexity of maintaining the value of any symmetric function on the prefixes of a bit string.