Smaller Cuts, Higher Lower Bounds

This article proves strong lower bounds for distributed computing in the congest model, by presenting bit-gadget : a new technique constructing graphs with small cuts. The contribution of bit-gadgets is twofold. First, developing careful sparse graph constructions cuts extends known techniques to show near-linear bound diameter, result previously only dense graphs. Moreover, sparseness construction plays crucial role applying it approximations various distance computation problems, drastically improving over what can be obtained when using Second, are essential proving super-linear bounds, none which were prior this work. In fact, they allow us near-quadratic several such as exact minimum vertex cover or maximum independent set, well coloring its chromatic number. Such not limited NP-hard given two simple problems P, shown require quadratic and number rounds. All above optimal up logarithmic factors. addition, context, complexity all-pairs-shortest-paths problem discussed. Finally, that translate semi-streaming despite being very different nature.