One of the important challenges in circuit complexity is proving strong
lower bounds for constant-depth circuits. One possible approach to
this problem is to use the framework of Karchmer-Wigderson relations:
Karchmer and Wigderson (SIDMA 3(2), 1990) observed that for every Boolean
function $f$ there is a corresponding communication problem $\mathrm{KW}_{f}$,
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The universal relation is the communication problem in which Alice and Bob get as inputs two distinct strings, and they are required to find a coordinate on which the strings differ. The study of this problem is motivated by its connection to Karchmer-Wigderson relations, which are communication problems that are ... more >>>

We deterministically construct quasi-polynomial weights in quasi-polynomial time, such that in a given polytope with totally unimodular constraints, one vertex is isolated, i.e., there is a unique minimum weight vertex.
More precisely,
the property that we need is that every face of the polytope lies in an affine space defined ... more >>>