On Local Distributed Sampling and Counting

Feng, Weiming; Yin, Yitong

doi:10.1145/3212734.3212757

Cited by 13 publications

(11 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We need the following proposition, which explains the relation between the multiplicative form of decay in (26) and the additive form of decay in (6). Similar results appeared in [1,2,17,48].…”

Section: Analysis Of Strong Spatial Mixingmentioning

confidence: 65%

Perfect sampling from spatial mixing

Feng

Guo

Yin

2022

Random Struct Algorithms

Self Cite

View full text Add to dashboard Cite

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with subexponential neighborhood growth like ℤd, our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer‐dimer models in such graphs.

show abstract

Section: Analysis Of Strong Spatial Mixingmentioning

confidence: 65%

Perfect sampling from spatial mixing

Feng

Guo

Yin

2022

Random Struct Algorithms

Self Cite

View full text Add to dashboard Cite

show abstract

“…(1) the SSM usually holds with respect to logarithmic potential functions [1,32,11]; (2) in [8], a local self-reduction is constructed to show that for self-reducible classes of spin systems, SSM with additive error can be boosted to the SSM with multiplicative error.…”

Section: List Coloring and Our Resultsmentioning

confidence: 99%

Perfect sampling from spatial mixing

Feng¹,

Guo²,

Yin³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We show that strong spatial mixing with a rate faster than the growth of neighborhood implies the existence of efficient perfect samplers for spin systems. Our new resampling based algorithm bypasses a major barrier of previous work along this line, namely that our algorithm works for general spin systems and does not require additional structures of the problem. In addition, our framework naturally incorporates spatial mixing properties to obtain linear expected running time. Using this new technique, we give the currently best perfect sampling algorithms for colorings in bounded degree graphs and in graphs with sub-exponential neighborhood growth.

show abstract

“…The Lazy Local Metropolis algorithm in above two theorems is communication-and computationefficient: each message consists of at most O(log n) bits and all local computations are fairly cheap. In a concurrent work [16], through network decomposition [22,38], a O(log 3 n)-round algorithm is given for sampling proper q-colorings of triangle-free graphs with maximum degree ∆ assuming q ≥ (α * + δ)∆, however, with messages of unbounded sizes and unbounded local computations.…”

Section: Resultsmentioning

confidence: 99%

Distributed Symmetry Breaking in Sampling (Optimal Distributed Randomly Coloring with Fewer Colors)

Feng,

Hayes,

Yin

2018

Preprint

Self Cite

View full text Add to dashboard Cite

We examine the problem of almost-uniform sampling proper q-colorings of a graph whose maximum degree is ∆. A famous result, discovered independently by Jerrum [31] and Salas and Sokal [39], is that, assuming q > (2+δ)∆, the Glauber dynamics (a.k.a. single-site dynamics) for this problem has mixing time O(n log n), where n is the number of vertices, and thus provides a nearly linear time sampling algorithm for this problem. A natural question is the extent to which this algorithm can be parallelized. Previous work [15] has shown that a O(∆ log n) time parallelized algorithm is possible, and that Ω(log n) time is necessary.We give a distributed sampling algorithm, which we call the Lazy Local Metropolis Algorithm, that achieves an optimal parallelization of this classic algorithm. It improves its predecessor, the Local Metropolis algorithm of Feng, Sun and Yin [PODC'17], by introducing a step of distributed symmetry breaking that helps the mixing of the distributed sampling algorithm.For sampling almost-uniform proper q-colorings of graphs G on n vertices, we show that the Lazy Local Metropolis algorithm achieves an optimal O(log n) mixing time if either of the following conditions is true for an arbitrary constant δ > 0:• q ≥ (2 + δ)∆, on general graphs with maximum degree ∆;• q ≥ (α * + δ)∆, where α * ≈ 1.763 satisfies α * = e 1/α * , on graphs with sufficiently large maximum degree ∆ ≥ ∆ 0 (δ) and girth at least 9.

show abstract

On Local Distributed Sampling and Counting

Abstract: *

Cited by 13 publications

References 23 publications

Perfect sampling from spatial mixing

Perfect sampling from spatial mixing

Perfect sampling from spatial mixing

Distributed Symmetry Breaking in Sampling (Optimal Distributed Randomly Coloring with Fewer Colors)

Contact Info

Product

Resources

About