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Faster Deterministic and Randomized Algorithms on the Homogeneous Set Sandwich Problem

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Experimental and Efficient Algorithms (WEA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3059))

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Abstract

A homogeneous set is a non-trivial, proper subset of a graph’s vertices such that all its elements present exactly the same outer neighborhood. Given two graphs, G 1(V,E 1), G 2(V,E 2), we consider the problem of finding a sandwich graph G s (V,E S ), with E 1 ⊆ E s  ⊆ E 2, which contains a homogeneous set, in case such a graph exists. This is called the Homogeneous Set Sandwich Problem (HSSP). We give an O(n 3.5) deterministic algorithm, which updates the known upper bounds for this problem, and an O(n 3) Monte Carlo algorithm as well. Both algorithms, which share the same underlying idea, are quite easy to be implemented on the computer.

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Author information

Authors and Affiliations

  1. Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Brazil

    Celina M. H. de Figueiredo, Guilherme D. da Fonseca & Vinícius G. P. de Sá

  2. Computer Science Department, Vanderbilt University, USA

    Jeremy Spinrad

Authors
  1. Celina M. H. de Figueiredo
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  2. Guilherme D. da Fonseca
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  3. Vinícius G. P. de Sá
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  4. Jeremy Spinrad
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Universidade Federal Fluminense, Rua Passo da Pátria, 156, Bloco E, RJ 24210-240, Niterói, Brazil

    Celso C. Ribeiro

  2. Departamento de Ciência da Computação, Universidade Federal Fluminense, Niterói, RJ, Brazil

    Simone L. Martins

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© 2004 Springer-Verlag Berlin Heidelberg

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de Figueiredo, C.M.H., da Fonseca, G.D., de Sá, V.G.P., Spinrad, J. (2004). Faster Deterministic and Randomized Algorithms on the Homogeneous Set Sandwich Problem. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_18

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  • DOI: https://doi.org/10.1007/978-3-540-24838-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22067-1

  • Online ISBN: 978-3-540-24838-5

  • eBook Packages: Springer Book Archive

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