Digraph Realization Problem: Difference between revisions
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(Created page with "{{DISPLAYTITLE: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 Realiza...") |
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== Parameters == | == Parameters == | ||
$n$: number of degree pairs | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Graph Realization Problems - Digraph Realization Problem - Time.png|1000px]] | [[File:Graph Realization Problems - Digraph Realization Problem - Time.png|1000px]] | ||
== References/Citation == | == References/Citation == | ||
https://linkinghub.elsevier.com/retrieve/pii/0012365X7390037X | https://linkinghub.elsevier.com/retrieve/pii/0012365X7390037X | ||
Latest revision as of 09:10, 28 April 2023
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