We revisit classical geometric search problems under the assumption of rational coordinates. Our main result is a tight bound for point separation, ie, to determine whether n given...
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 t...
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bo...
We establish the first nontrivial lower bounds on timespace tradeoffs for the selection problem. We prove that any comparison-based randomized algorithm for finding the median ...
We show that any deterministic data-stream algorithm that makes a constant number of passes over the input and gives a constant factor approximation of the length of the longest i...