Unique Games Conjecture (UGC), proposed by [24], lies in the center of many inapproximability results. At the heart of UGC lies approximability of MAX-CUT, which is a special instance of Unique Game. [25, 29] showed that assuming Unique Games Conjecture, it is NPhard to distinguish between MAX-CUT instance that has a value 1 − ε vs. 1 − Ω( √ ε). [14] then showed a matching polynomial time algor...

This report describes our test on using statistical translation models for bilingual IR tasks in CLEF-2001. These translation models have been trained on a set of parallel web pages automatically mined from the Web. Our goal is to compare the following approaches: using the original parallel corpora or a cleaned corpora to train translation models; using the raw translation probabilities to wei...

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper we provide the first algorithmic applications of tree-cut width to hard combinatorial problems. Tree-cut width is known to be lower-bounded by a function of treewidth, but it can be much larger and hence has the poten...

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what will call Cut-for-Formulas Cut-for-Sets Theorem: for a set F and binary relation ⊢ on P ( ) $\mathcal {P}(F)$ , if finitary, monotonic, satisfies cut formulas, then it also sets. deduce CF/CS from Ultrafilter twice; each proof uses different order-theoretic variant of Tukey-Teichmüller...

Abstract Let V be a set of n vertices, $${\mathcal M}$$ M m labels, and let $${\textbf{R}}$$ R an $$m \times n$$ m × n matrix ofs independent Bernoulli random variables with probability success p ; columns are incidence...