Storing Set Families More Compactly with Top ZDDs

04/09/2020
by   Kotaro Matsuda, et al.
0

Zero-suppressed Binary Decision Diagrams (ZDDs) are data structures for representing set families in a compressed form. With ZDDs, many valuable operations on set families can be done in time polynomial in ZDD size. In some cases, however, the size of ZDDs for representing large set families becomes too huge to store them in the main memory. This paper proposes top ZDD, a novel representation of ZDDs which uses less space than existing ones. The top ZDD is an extension of top tree, which compresses trees, to compress directed acyclic graphs by sharing identical subgraphs. We prove that navigational operations on ZDDs can be done in time poly-logarithmicin ZDD size, and show that there exist set families for which the size of the top ZDD is exponentially smaller than that of the ZDD. We also show experimentally that our top ZDDs have smaller size than ZDDs for real data.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/11/2018

Enumerating All Subgraphs without Forbidden Induced Subgraphs via Multivalued Decision Diagrams

We propose a general method performed over multivalued decision diagrams...
research
07/15/2022

On the number of terms of some families of the ternary cyclotomic polynomials Φ_3p_2p_3

We study the number of non-zero terms in two specific families of ternar...
research
11/26/2020

Tight Bound on Vertex Cut Sparsifiers in Directed Acyclic Graphs

For an unweighted graph on k terminals, Kratsch and Wahlström constructe...
research
10/11/2021

Parallel Batched Interpolation Search Tree

Ordered set (and map) is one of the most used data type. In addition to ...
research
02/20/2020

Compressed Data Structures for Binary Relations in Practice

Binary relations are commonly used in Computer Science for modeling data...
research
01/02/2022

Implicit representation of sparse hereditary families

For a hereditary family of graphs , let _n denote the set of all members...
research
11/24/2020

Fiedler vector analysis for particular cases of connected graphs

In this paper, some subclasses of block graphs are considered in order t...

Please sign up or login with your details

Forgot password? Click here to reset