Rapid Mixing of Hypergraph Independent Set

نویسندگان

  • Jonathan Hermon
  • Allan Sly
  • Yumeng Zhang
چکیده

We prove that the the mixing time of the Glauber dynamics for sampling independent sets on n-vertex k-uniform hypergraphs is Opn log nq when the maximum degree ∆ satisfies ∆ ď c2k{2, improving on the previous bound [BDK06] of ∆ ď k ́ 2. This result brings the algorithmic bound to within a constant factor of the hardness bound of [BGG`16] which showed that it is NP-hard to approximately count independent sets on hypergraphs when ∆ ě 5 ̈ 2k{2.

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

Metric Construction, Stopping Times and Path Coupling

In this paper we examine the importance of the choice of metric in path coupling, and the relationship of this to stopping time analysis. We give strong evidence that stopping time analysis is no more powerful than standard path coupling. In particular, we prove a stronger theorem for path coupling with stopping times, using a metric which allows us to restrict analysis to standard one-step pat...

متن کامل

An Eecient Parallel Algorithm for Computing a Maximal Independent Set in a Hypergraph of Dimension 3

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and...

متن کامل

An Efficient Parallel Algorithm for Computing a Maximal Independent Set in a Hypergraph of Dimension 3

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and...

متن کامل

Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We give a new method for analysing the mixing time of a Markov chain using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree ∆ of a vertex and the minimum size m of an edge satisfy m ≥ 2∆ + 1. We also show that the Glauber dynamics for proper q-c...

متن کامل

Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree ∆ of a vertex and the minimum size m of an edge satisfy m ≥ 2∆+1. We also show that the Glauber dynamics for proper q-colourings of a hypergraph m...

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:
  • CoRR

دوره abs/1610.07999  شماره 

صفحات  -

تاریخ انتشار 2016