DAG Realization Problem (Graph Realization Problems)

Description

Given a sequence $S := (a_1, b_1), \ldots, (a_n, b_n)$ with $a_i, b_i \in \mathbb{Z}_0^+$, does there exist a directed acyclic graph (DAG) (no parallel arcs allowed) with labeled vertex set $V := \{v_1, \ldots , v_n\}$ such that for all $v_i \in V$ indegree and outdegree of $v_i$ match exactly the given numbers $a_i$ and $b_i$, respectively?

Related Problems

Generalizations: Digraph Realization Problem

Parameters

$n$: number of degree pairs

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Berger & Müller-Hannemann	2011	$O(\exp(n)$)	?	Exact	Deterministic	Time

Time Complexity Graph

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References/Citation

https://link.springer.com/chapter/10.1007/978-3-642-30870-3_29