Lower bounds for dynamic connectivity

We prove an (lg n) cell-probe lower bound on maintaining connectivity in dynamic graphs, as well as a more general trade-off between updates and queries. Our bound holds even if the graph is formed by disjoint paths, and thus also applies to trees and plane graphs. The bound is known to be tight for these restricted cases, proving optimality of these data structures (e.g., Sleator and Tarjan's dynamic trees). Our trade-off is known to be tight for trees, and the best two data structures for dynamic connectivity in general graphs are points on our trade-off curve. In this sense these two data structures are optimal, and this tightness serves as strong evidence that our lower bounds are the best possible. From a more theoretical perspective, our result is the first logarithmic cell-probe lower bound for any problem in the natural class of dynamic language membership problems, breaking the long standing record of (lg n/ lg lg n). In this sense, our result is the first data-structure...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Mihai Patrascu, Erik D. Demaine
• Keywords: Algorithms, Cell-probe Lower Bound, Data Structures, Long Standing Record, STOC 2004