Calculating lower bounds for caching problems

Lower Bounds for Covering Problems

Some Lower Bounds for Estrada Index

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 Combinatorial Problems on Graphs

Nontrivial lower bounds are given for the computation time of various combinatorial problems on graphs under a linear or algebraic decision tree model. An SI( n310g n) bound is obtained for a “travelling salesman problem” on a weighted complete graph of n vertices. Moreover it is shown that the same bound is valid for the “subgraph detection problem” with respect to property P if P is hereditar...

Lower Bounds for Two Call Control Problems

We present lower bounds for two call control scheduling problems. For the problem of scheduling innnite-duration calls deterministically without pre-emption on a linear array of processors, in which the goal is to use as many edges as possible, we show a 2 + 1 4:2 lower bound on the competitive ratio (where is the golden ratio). For the problem of scheduling innnite-duration calls on an edge of...