Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Data Structures and Algorithms

arXiv:1912.01854 (cs)
[Submitted on 4 Dec 2019]

Title:Popular Branchings and Their Dual Certificates

Authors:Telikepalli Kavitha, Tamás Király, Jannik Matuschke, Ildikó Schlotter, Ulrike Schmidt-Kraepelin
View PDF
Abstract:Let $G$ be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed forests; a branching $B$ is popular if $B$ does not lose a head-to-head election (where nodes cast votes) against any branching. Such popular branchings have a natural application in liquid democracy. The popular branching problem is to decide if $G$ admits a popular branching or not. We give a characterization of popular branchings in terms of dual certificates and use this characterization to design an efficient combinatorial algorithm for the popular branching problem. When preferences are weak rankings, we use our characterization to formulate the popular branching polytope in the original space and also show that our algorithm can be modified to compute a branching with least unpopularity margin. When preferences are strict rankings, we show that "approximately popular" branchings always exist.
Subjects: Data Structures and Algorithms (cs.DS); Computer Science and Game Theory (cs.GT)
Cite as: arXiv:1912.01854 [cs.DS]
  (or arXiv:1912.01854v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.1912.01854

Submission history

From: Ulrike Schmidt-Kraepelin [view email]
[v1] Wed, 4 Dec 2019 09:08:12 UTC (43 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cs.DS
< prev   |   next >
new | recent | 2019-12
Change to browse by:
cs
cs.GT

References & Citations

DBLP - CS Bibliography

listing | bibtex
Telikepalli Kavitha
Tamás Király
Jannik Matuschke
Ildikó Schlotter
Ulrike Schmidt-Kraepelin
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)