Skip to main content
Springer Nature Link
Log in

Exact Algorithms for Induced Subgraph Problems

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 163 Accesses

Years and Authors of Summarized Original Work

  • 2010; Fomin, Villanger

  • 2013; Bliznets, Fomin, Pilipczuk, Villanger

Problem Definition

A graph class Π is a set of simple graphs. One can also think of Π as a property: Π comprises all the graphs that satisfy a certain condition. We say that class (property) Π is hereditary if it is closed under taking induced subgraphs. More precisely, whenever G ∈ Π and H is an induced subgraph of G, then also H ∈ Π.

We shall consider the Maximum InducedΠ-Subgraph problem: given a graph G, find the largest (in terms of the number of vertices) induced subgraph of G that belongs to Π. Suppose now that class Π is polynomial-time recognizable: there exists an algorithm that decides whether a given graph H belongs to Π in polynomial time. Then Maximum InducedΠ-Subgraph on an n-vertex graph G can be solved by brute force in time (The \(\mathcal{O}^{\star }(\cdot )\) notation hides factors polynomial in the input size.) \(\mathcal{O}^{\star }(2^{n})\): we...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. Bliznets I, Fomin FV, Pilipczuk M, Villanger Y (2013) Largest chordal and interval subgraphs faster than 2n. In: Bodlaender HL, Italiano GF (eds) ESA, Sophia Antipolis. Lecture Notes in Computer Science, vol 8125. Springer, pp 193–204

    Google Scholar 

  2. Fomin FV, Villanger Y (2010) Finding induced subgraphs via minimal triangulations. In: Marion JY, Schwentick T (eds) STACS, Nancy. LIPIcs, vol 5. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik, pp 383–394

    Google Scholar 

  3. Fomin FV, Gaspers S, Kratsch D, Liedloff M, Saurabh S (2010) Iterative compression and exact algorithms. Theor Comput Sci 411(7–9):1045–1053

    Article  MathSciNet  MATH  Google Scholar 

  4. Fomin FV, Todinca I, Villanger Y (2011) Exact algorithm for the maximum induced planar subgraph problem. In: Demetrescu C, Halldórsson MM (eds) ESA, Saarbrücken. Lecture notes in computer science, vol 6942. Springer, pp 287–298

    Google Scholar 

  5. Fomin FV, Todinca I, Villanger Y (2014) Large induced subgraphs via triangulations and CMSO. In: Chekuri C (ed) SODA, Portland. SIAM, pp 582–583

    Google Scholar 

  6. Gaspers S, Kratsch D, Liedloff M (2012) On independent sets and bicliques in graphs. Algorithmica 62(3–4):637–658

    Article  MathSciNet  MATH  Google Scholar 

  7. Gupta S, Raman V, Saurabh S (2012) Maximum r-regular induced subgraph problem: fast exponential algorithms and combinatorial bounds. SIAM J Discr Math 26(4):1758–1780

    Article  MathSciNet  MATH  Google Scholar 

  8. Pilipczuk M, Pilipczuk M (2012) Finding a maximum induced degenerate subgraph faster than 2n. In: Thilikos DM, Woeginger GJ (eds) IPEC, Ljubljana. Lecture notes in computer science, vol 7535. Springer, pp 3–12

    Google Scholar 

  9. Raman V, Saurabh S, Sikdar S (2007) Efficient exact algorithms through enumerating maximal independent sets and other techniques. Theory Comput Syst 41(3):563–587

    Article  MathSciNet  MATH  Google Scholar 

  10. Robson JM (1986) Algorithms for maximum independent sets. J Algorithms 7(3):425–440

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Warsaw, University of Warsaw, Warsaw, Poland

    Michał Pilipczuk

  2. University of Bergen, University of Bergen, Bergen, Norway

    Michał Pilipczuk

Authors
  1. Michał Pilipczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michał Pilipczuk .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Pilipczuk, M. (2016). Exact Algorithms for Induced Subgraph Problems. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_520

Download citation

Publish with us

Policies and ethics