Probabilistically Checkable Proofs and Approximating Solutions to Hard Problems

نویسنده

  • Kyle Littlefield
چکیده

2 A Brief Introduction to Theory of Computation 3 2.1 Some Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Modelling Computation Turing Machines . . . . . . . . . . . . 3 2.3 NP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Sample NP Problems . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Optimizations for NP Problems . . . . . . . . . . . . . . . . . . . 9

برای دانلود رایگان 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

How NP got a new definition: a survey of probabilistically checkable proofs

We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class NP, and imply that computing approximate solutions to many NP-hard problems is itself NP-hard. Techniques developed to prove them have had many other consequences. 2000 Mathematics Subject Classification: 68Q10, 68Q15, 68Q17, 68Q25.

متن کامل

Lecture 16 — November 6 th , 2012 ( Prasad Raghavendra )

In this lecture, we will begin to talk about the “PCP Theorem” (Probabilistically Checkable Proofs Theorem). Since the discovery of NP-completeness in 1972, researchers had mulled over the issue of whether we can efficiently compute approximate solutions to NP-hard optimization problems. They failed to design such approximate algorithms for most problems. They then tried to show that computing ...

متن کامل

Cs880: Approximations Algorithms 29.1 Vertex Cover

In the previous lecture we introduced probabilistically checkable proofs (PCPs) and saw how they could be used to obtain a tight inapproximability result for MAX-3SAT. We also introduced Hastad’s 3-bit PCP, a very useful tool for proving inapproximability results. In this lecture we apply Hastad’s 3-bit PCP to show that approximating Vertex Cover within any constant factor less than 7/6 is NP-h...

متن کامل

Zero Knowledge and the

We present a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max-3-coloring and max-3-sat, showing that it is hard to approximate the chromatic number within (N), for some > 0. We then apply our technique in conjunction with the probabilistically che...

متن کامل

Zero Knowledge and the Chromatic

We present a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max-3-coloring and max-3-sat, showing that it is hard to approximate the chromatic number within (N), for some > 0. We then apply our technique in conjunction with the probabilistically che...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005