Bypassing UGC from Some Optimal Geometric Inapproximability Results

Some Optimal Inapproximability Results

On Some Tighter Inapproximability Results

We give a number of improved inapproximability results, including the best up to date explicit approximation thresholds for bounded occurence satis ability problems like MAX2SAT and E2-LIN-2, and the bounded degree graph problems, like MIS, Node Cover, and MAX CUT. We prove also for the rst time inapproximability of the problem of Sorting by Reversals and display an explicit approximation thres...

On Some Tighter Inapproximability Results, Further Improvements

Improved inaproximability results are given, including the best up to date explicit approximation thresholds for bounded occurence sat-issability problems, like MAX-2SAT and E2-LIN-2, and problems in bounded degree graphs, like MIS, Node Cover and MAX CUT. We prove also for the rst time inapproximability of the problem of Sorting by Reversals and display an explicit approximation threshold for ...

Some Geometric Results Arising from the Borel Fixed Property

In this paper, we will give some geometric results using generic initial ideals for the degree reverse lex order. The first application is to the regularity of a Cohen-Macaulay algebra, and we improve a well-known bound. The main goal of the paper, though, is to improve on results of Bigatti, Geramita and Migliore concerning geometric consequences of maximal growth of the Hilbert function of th...

Inapproximability Some history and some open problems

The purpose of this talk is to give an overview of the status of some problems in approximability.