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Exact Algorithms for Induced Subgraph Problems

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Encyclopedia of Algorithms

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 INDUCED Π -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 INDUCED Π -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...

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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

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  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

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  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

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

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  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

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

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  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

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  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

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  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

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Authors and Affiliations

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

    MichaƂ Pilipczuk

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  1. MichaƂ Pilipczuk
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Correspondence to MichaƂ Pilipczuk .

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Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Pilipczuk, M. (2015). Exact Algorithms for Induced Subgraph Problems. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_520-1

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_520-1

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  • Publisher Name: Springer, Boston, MA

  • Online ISBN: 978-3-642-27848-8

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