We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time.

In the square packing problem, the goal is to pack squares of different sizes into the smallest number of bins (squares) of uniform size. We introduce an almostonline square packing algorithm which places squares in an online, sequential manner. In doing so, it receives advice of logarithmic size from an offline oracle which runs in linear time. Our algorithm achieve a competitive ratio of at m...

We introduce a new geometric tool for analyzing groups of finite au-tomata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reproduc...