Approximating the Permanent with Deep Rejection Sampling

08/16/2021
by   Juha Harviainen, et al.
0

We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the upper bound for the permanent with a linear combination of the subproblem bounds at a moderately large depth of the recursion tree. This method, we call deep rejection sampling, is empirically shown to outperform the basic, depth-zero variant, as well as a related method by Kuck et al. (NeurIPS 2019). We analyze the expected running time of the scheme on random (0, 1)-matrices where each entry is independently 1 with probability p. Our bound is superior to a previous one for p less than 1/5, matching another bound that was known to hold when every row and column has density exactly p.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/03/2020

Near-Optimal Entrywise Sampling of Numerically Sparse Matrices

Many real-world data sets are sparse or almost sparse. One method to mea...
research
11/03/2018

Tight complexity lower bounds for integer linear programming with few constraints

We consider the ILP Feasibility problem: given an integer linear program...
research
03/25/2019

A linear bound on the k-rendezvous time for primitive sets of NZ matrices

A set of nonnegative matrices is called primitive if there exists a prod...
research
03/22/2015

Relaxed Leverage Sampling for Low-rank Matrix Completion

We consider the problem of exact recovery of any m× n matrix of rank ϱ f...
research
02/02/2019

Finite-Blocklength Performance of Sequential Transmission over BSC with Noiseless Feedback

In this paper, we consider the expected blocklength of variable-length c...
research
12/21/2021

Lower Bounds for Sparse Oblivious Subspace Embeddings

An oblivious subspace embedding (OSE), characterized by parameters m,n,d...
research
11/26/2019

Approximating the Permanent by Sampling from Adaptive Partitions

Computing the permanent of a non-negative matrix is a core problem with ...

Please sign up or login with your details

Forgot password? Click here to reset