Algorithms and Complexity Group
  • People
  • Research
  • Courses
  • Talks
  • Jobs
  • Contact

BranchLIS: a tool for computing branch decompositions of graphs and hypergraphs with SAT-based local improvement

Various decomposition techniques have proven to be useful for efficient solving of many hard problems, e.g., the #P-complete problem of counting models for a propositional formula, albeit there is an exponential dependency on the width measures that are associated with these decompositions. Therefore, it is of interest to obtain decompositions of small width. There are various exact methods, approximations, and heuristics which allow us to compute the decompositions. The exact methods can be only used for very small problem instances and are generally slow, whereas the approximations and heuristic methods are usually fast but far off from the optimal widths. SAT-based local improvements try to use the speed of the heuristics and use exact methods to get better upper bounds for a given width parameter.

Branch decomposition is a prominent method for structurally decomposing a graph, hypergraph or CNF formula. The width of a branch decomposition provides a measure of how well the object is decomposed. We propose BranchLIS, a SAT approach to finding branch decompositions of small width.

SAT Encoding for Branchwidth

The core of our approach is an efficient SAT encoding which determines with a single SAT-call whether a given hypergraph admits a branch decomposition of a certain width. For our encoding, we developed a novel partition-based characterization of branch decomposition. Using this encoding we can obtain optimal widths for small instances as well as an upper bound for larger instances.

SAT-based Local Improvement for Branchwidth

The encoding size imposes a limit on the size of the input hypergraph. In order to break through this barrier and to scale the SAT approach to larger instances, we developed a new heuristic approach (BranchLIS) where the SAT encoding is used to locally improve a given candidate decomposition until a fixed-point is reached. This new method scales now to instances with several thousands of vertices and edges.

Downloads

The source code can be downloaded from GitHub. BranchLIS is written in Python2.7 and requires Python library Networkx. BranchLIS can also be used for visualizing the graphs and their decomposition (requires matplotlib).

Team

Neha Lodha, Sebastian Ordyniak, Stefan Szeider

Developer

Neha Lodha

Publications

2 results
2017
[2]A SAT Approach to Branchwidth
Neha Lodha, Sebastian Ordyniak, Stefan Szeider
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017 (Carles Sierra, ed.), pages 4894–4898, 2017, ijcai.org.
Note: Sister Conference Best Paper Track
[bibtex] [pdf] [doi]
2016
[1]A SAT Approach to Branchwidth
Neha Lodha, Sebastian Ordyniak, Stefan Szeider
Theory and Applications of Satisfiability Testing - SAT 2016 - 19th International Conference, Bordeaux, France, July 5-8, 2016, Proceedings (Nadia Creignou, Daniel Le Berre, eds.), volume 9710 of Lecture Notes in Computer Science, pages 179–195, 2016, Springer Verlag.
[bibtex] [doi]

 

 

News

  • Martin Nöllenburg: promotion to Full Professor

    Martin Nöllenburg: promotion to Full Professor

    2020-12-17
    By December 1st, 2020, our colleague Martin Nöllenburg has been promoted to Full Professor for Graph and Geometric Algorithms.  Martin has …Read More »
  • Martin Kronegger wins the Best Teaching Award 2020

    Martin Kronegger wins the Best Teaching Award 2020

    2020-10-23
    Congratulations to Martin Kronegger who received a Best Teaching Award 2020 from TU Wien. The Algorithms and Complexity group is …Read More »
  • Welcome to our Feodor Lynen Fellow Dr. Manuel Sorge

    Welcome to our Feodor Lynen Fellow Dr. Manuel Sorge

    2020-10-12
    On October 1, 2020, Dr. Manuel Sorge has joined the Algorithms and Complexity group with a prestigious Feodor Lynen postdoc …Read More »
  • TU Wien students excel at the 2020 Graph Drawing Contest

    TU Wien students excel at the 2020 Graph Drawing Contest

    2020-10-01
    The 27th annual Graph Drawing Contest, held (virtually) in conjunction with the 28th International Symposium on Graph Drawing and Network …Read More »
  • Best Paper Award at CP’2020

    Best Paper Award at CP’2020

    2020-09-11
    Tomáš Peitl and Stefan Szeider won the Best Paper Award at the main track of CP'2020, the 26th International Conference on Principles …Read More »

News archive

All news for 2015, 2016, 2017, 2018 and 2019.
TU Wien Informatics
Offenlegung (§25 MedienG) Inhaber der Website ist das Institut für Logic and Computation an der Technischen Universität Wien, 1040 Wien. Die TU Wien distanziert sich von den Inhalten aller extern gelinkten Seiten und übernimmt diesbezüglich keine Haftung. – Disclaimer – Datenschutzerklärung
Log in requires cookies.