Polynomial Kernels for Weighted Problems

نویسندگان

  • Michael Etscheid
  • Stefan Kratsch
  • Matthias Mnich
  • Heiko Röglin
چکیده

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for Subset Sum and Knapsack when parameterized by the number n of items. We answer both questions affirmatively by using an algorithm for compressing numbers due to Frank and Tardos (Combinatorica 1987). This result had been first used by Marx and Végh (ICALP 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for Subset Sum and an exponential kernelization for Knapsack. Finally, we also obtain kernelization results for polynomial integer programs.

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

An ‎E‎ffective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...

متن کامل

Evaluation of Sentinel-1 Interferometric SAR Coherence efficiency for Land Cover Mapping

In this study, the capabilities of Interferometric Synthetic Aperture Radar (InSAR) time series data and machine learning have been evaluated for land cover mapping in Iran. In this way, a time series of Sentinel-1 SAR data (including 16 SLC images with approximately 24 days time interval) from 2018 to 2020 were used for a region of Ahvaz County located in Khuzestan province. Using InSAR proces...

متن کامل

On the Equivalence of the Weighted Least Squares and the Generalised Least Squares Estimators, with Applications to Kernel Smoothing

The paper establishes the conditions under which the generalised least squares estimator of the regression parameters is equivalent to the weighted least squares estimator. The equivalence conditions have interesting applications in local polynomial regression and kernel smoothing. Specifically, they enable to derive the optimal kernel associated with a particular covariance structure of the me...

متن کامل

Polynomial kernels collapse the W-hierarchy

We prove that, for many parameterized problems in the class FPT, the existence of polynomial kernels implies the collapse of the Whierarchy (i.e., W[P] = FPT). The collapsing results are also extended to assumed exponential kernels for problems in the class FPT. In particular, we establish a close relationship between polynomial (and exponential) kernelizability and the existence of sub-exponen...

متن کامل

Kernelization Lower Bounds By Cross-Composition

We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L and/or-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially bounded parameter value that expresses the logical and or or of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a re...

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:
  • J. Comput. Syst. Sci.

دوره 84  شماره 

صفحات  -

تاریخ انتشار 2015