Paper Info
Title
Approximately counting and sampling small witnesses using a colourful decision oracle.
Abstract
In this paper, we prove "black box" results for turning algorithms which decide whether or not a witness exists into algorithms to approximately count the number of witnesses, or to sample from the set of witnesses approximately uniformly, with essentially the same running time. We do so by extending the framework of Dell and Lapinskas (STOC 2018), which covers decision problems that can be expressed as edge detection in bipartite graphs given limited oracle access; our framework covers problems which can be expressed as edge detection in arbitrary k-hypergraphs given limited oracle access. (Simulating this oracle generally corresponds to invoking a decision algorithm.) This includes many key problems in both the fine-grained setting (such as k-SUM, k-OV and weighted k-Clique) and the parameterised setting (such as induced subgraphs of size k or weight-k solutions to CSPs). From an algorithmic standpoint, our results will make the development of new approximate counting algorithms substantially easier; indeed, it already yields a new state-of-the-art algorithm for approximately counting graph motifs, improving on Jerrum and Meeks (JCSS 2015) unless the input graph is very dense and the desired motif very small. Our k-hypergraph reduction framework generalises and strengthens results in the graph oracle literature due to Beame et al. (ITCS 2018) and Bhattacharya et al. (CoRR abs/1808.00691).
Year
DOI
Venue
2020
10.5555/3381089.3381224
SODA '20: ACM-SIAM Symposium on Discrete Algorithms Salt Lake City Utah January, 2020
Field
DocType
Citations 
Discrete mathematics,Computer science,Oracle,Arithmetic,Sampling (statistics)
Conference
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Holger Dell122016.74
John Lapinskas2134.25
Kitty Meeks3448.20