On Dynamic Bit-Probe Complexity

This paper presents several advances in the understanding of dynamic data structures in the bit-probe model: – We improve the lower bound record for dynamic language membership problems to Ω(( lg n lg lg n )2 ). Surpassing Ω(lg n) was listed as the first open problem in a survey by Miltersen. – We prove a bound of Ω( lg n lg lg lg n ) for maintaining partial sums in Z/2Z. In the course of the proof, we show how to use the chronogram technique to obtain logarithmic bounds in the cell-probe model. This is an important methodological progress, even though such bounds were obtained recently through a different technique. – We prove a surprising and tight upper bound of O( lg n lg lg n ) for predecessor problems. We use this to obtain the same upper bound for dynamic word and prefix problems in group-free monoids.

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Corina E. Patrascu, Mihai Patrascu
• Keywords: Dynamic Data Structures, ICALP 2005, Lower Bound Record, Theoretical Computer Science, Upper Bound