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 >>>

We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not \subseteq$DTIME$(2^{{\log^{O(1/\epsilon)} n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\log ^{1-\epsilon}n}.$ This improves upon the previous hardness factor of $(\log n)^\delta$ for some $\delta ... more >>>

In this paper we demonstrate a close connection between UniqueGames and
MultiCut.
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In MultiCut, one is given a ``network graph'' and a ``demand
graph'' on the same vertex set and the goal is to remove as few
edges from the network graph as ... more >>>

In this paper we will be concerned with a large class of packing
and covering problems which includes Vertex Cover and Independent Set.
Typically, for NP-hard problems among them, one can write an LP relaxation and
then round the solution. For instance, for Vertex Cover, one can obtain a
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