Digraph 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 graph (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

Subproblem: DAG Realization Problem

Parameters

$n$: number of degree pairs

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Kleitman–Wang Algorithm	1973	$O(n)$	$O(n)$	Exact	Deterministic	Time
Fulkerson–Chen–Anstee	1982	$O(n)$	$O({1})$	Exact	Deterministic	Time

Time Complexity graph

Space Complexity graph

Pareto Decades graph

References/Citation

https://linkinghub.elsevier.com/retrieve/pii/0012365X7390037X