DAG Realization Problem: Difference between revisions
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(Created page with "{{DISPLAYTITLE: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...") |
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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 - DAG Realization Problem - Time.png|1000px]] | [[File:Graph Realization Problems - DAG Realization Problem - Time.png|1000px]] | ||
Latest revision as of 13:04, 15 February 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 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.ezproxy.canberra.edu.au/chapter/10.1007/978-3-642-30870-3_29