Approximation Hardness for Small Occurrence Instances of NP-Hard Problems

نویسندگان

  • Miroslav Chlebík
  • Janka Chlebíková
چکیده

The paper contributes to the systematic study (started by Berman and Karpinski) of explicit approximability lower bounds for small occurrence optimization problems. We present parametrized reductions for some packing and covering problems, including 3-Dimensional Matching, and prove the best known inapproximability results even for highly restricted versions of them. For example, we show that it is NPhard to approximate Max-3-DM within 139 138 even on instances with exactly two occurrences of each element. Previous known hardness results for bounded occurence case of the problem required that the bound is at least three, and even then no explicit lower bound was known. New structural results which improve the known bounds for 3-regular amplifiers and hence the inapproximability results for numerous small occurrence problems studied earlier by Berman and Karpinski are also presented.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Nov 15 & 17 , 2011 ) : Hardness of Approximation , PCP theorem

So far we have been mostly talking about designing approximation algorithms and proving upper bounds. From no until the end of the course we will be talking about proving lower bounds (i.e. hardness of approximation). We are familiar with the theory of NP-completeness. When we prove that a problem is NP-hard it implies that, assuming P 6=NP there is no polynomail time algorithm that solves the ...

متن کامل

Approximating Bounded Degree Instances of NP-Hard Problems

We present some of the recent results on computational complexity of approximating bounded degree combinatorial optimization problems. In particular, we present the best up to now known explicit nonapproximability bounds on the very small degree optimization problems which are of particular importance on the intermediate stages of proving approximation hardness of some other generic optimizatio...

متن کامل

On Approximability of Bounded Degree Instances of Selected Optimization Problems

In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation algorithms for the restricted version of the problem with improved performance guarantees. In this thesis, we investigate the approximation complexity of selected NP-hard opti...

متن کامل

On the Worst-Case Approximability of Sparse PCA

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1. a simple and efficient algorithm that achieves an n-approximation; 2. NP-hardness of approximation to within (1 − ε), for some small constant ε > 0; 3. SSE-hardness of approximation t...

متن کامل

On the Approximability of Sparse PCA

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1. a simple and efficient algorithm that achieves an n−1/3-approximation; 2. NP-hardness of approximation to within (1− ε), for some small constant ε > 0; 3. SSE-hardness of approximatio...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002