Lower Bounds for Dynamic Algebraic Problems

Lower Bounds for Dynamic Algebraic Problems

We consider dynamic evaluation of algebraic functions (matrix multiplication, determinant, convolution, Fourier transform, etc.) in the model of Reif and Tate; i.e., if f(x1, . . . , xn) = (y1, . . . , ym) is an algebraic problem, we consider serving on-line requests of the form “change input xi to value v” or “what is the value of output yi?”. We present techniques for showing lower bounds on ...

Lower Bounds For Algebraic Computation Trees

A topological method is given for obtaining lower bounds for the height of algebraic computation trees, and algebraic decision trees. Using this method we are able to generalize, and present in a uniform and easy way, almost all the known nonlinear lower bounds for algebraic computations. Applying the method to decision trees we extend all the apparently known lower bounds for linear decision t...

Lower Bounds for Covering Problems

Lower Bounds for Dynamic Connectivity

Our final goal here is to present a lower bound on the worst case time complexity of any data structure that solves this problem in the cell probe model of computation. The same idea, together with more careful analysis, can be used to establish a trade-off lower bound for this problem. For a data structure that solves dynamic connectivity (in cell probe model), assume the amortized update time...

Some Lower Bounds for Estrada Index