# Digraph Realization Problem (Graph Realization Problems)

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## 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

## References/Citation

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